help-39

[atomic pendant]

it didnt tell us that

i assumed it was a scalar

[fluid axle]

yeah ig they didn't

[atomic pendant]

ahhh so i see now a transpose becomes [2 1][x1; x2] = 3?

[fluid axle]

yeah

[atomic pendant]

2x1 + 1x2 = 3?

[fluid axle]

yeah

[atomic pendant]

so its just their mistake

or is that just obvious

for most people?

[fluid axle]

not obvious if you see it for the first time

[atomic pendant]

i thought vectors have the arrow on it

[fluid axle]

I just jumped right into it, cause ik what an hyperplane is alr

[fluid axle]

that's for highschoolers, so they don't get confused

[atomic pendant]

where did the y come from in your equation

theres only x

[fluid axle]

I just used x and y instead of x1 x2

just so that it looks more like the usual equations of lines

[atomic pendant]

why'd they give that hint? is there a way to see if it's convex through graphing it or something?

[fluid axle]

if you're able to graph a hyperplane in R^12 I'm all ears

[fluid axle]

it's just to get your mind going with a simple example

[atomic pendant]

wait is this a convex function or a convex set?

[fluid axle]

convex set

[atomic pendant]

cause i know for convex function we need all lines for all points to be above the function

[fluid axle]

there's no function here

[atomic pendant]

oh so then its a set so we just use that rule

for x, y in R^2 and a in [0, 1] ax + (1-a)y in r2?

[fluid axle]

that's to show R^2 is convex

but that's obvious

[atomic pendant]

oh i meant for x,y such that 2x, y = 3 i guess

but not sure

[fluid axle]

say H is your hyperplane, you want to show that
for all x, y in H, a in [0, 1], (1-a)x + ay in H

[atomic pendant]

im just confused because you say its a set but i can graph it too

[fluid axle]

well it is a set

quite literally

it's defined in set-builder notation

[atomic pendant]

oh so all the points that make up that functigon line

[fluid axle]

yea

[atomic pendant]

this seems doable i'll try it with the 2 dimentional one but my only curiosity is how i would do it for a general hyperplane now

[fluid axle]

just use the equation that defines the hyperplane

what does it mean for x and y to be in the hyperplane?

what does it mean for (1-t)x + ty to be in the hyperplace ?

[pearl pond]

@atomic pendant Has your question been resolved?

[pearl pond]

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[hushed galleon]

Hi I need to clarify something about bounds, so I have a set defined for n>=2 and I am to find the best upper bound and lower bound of the set does that mean i have to find sup(A) and inf(A) based on n or just based on the smallest and greatest over all values of n?

[regal herald]

just for each case n

[hushed galleon]

okay that makes more sense

thank you

.close

[pearl pond]

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[hushed galleon]

.reopen

[pearl pond]

✅

[hushed galleon]

I just realised that it says A_n so there are multiple sets so it was obvious

.close

[pearl pond]

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[mild tartan]

im on (c)

[pearl pond]

@mild tartan Has your question been resolved?

[regal herald]

what have you done so far

[pearl pond]

@mild tartan Has your question been resolved?

[pearl pond]

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[deft quiver]

jkj

[deft quiver]

How do I solve this step by step

.reopen

Wait jk

[pearl pond]

@deft quiver Has your question been resolved?

[rough forge]

Have you tried a substitution?

[deft quiver]

is u basically x?

[rough forge]

u is u

[deft quiver]

so wouldnt u be the substitution then?

[rough forge]

You wanna use another variable

other than u

x works, but the substitution u = x is useless

[deft quiver]

what would you suggest then

[jolly parrot]

bacc (unhelpful)

[deft quiver]

gotcha and then the derivative of that would be 3u^2 right?

[rough forge]

yes

[jolly parrot]

bacc (unhelpful)

[deft quiver]

when do i substitute that dertivate

[rough forge]

,, \dd u = \frac{1}{3u^2} : {\dd x}

[jolly parrot]

bacc (unhelpful)

[rough forge]

You also substitute the differential du

[deft quiver]

this is the part that i get stuck on lol

I dont know hwo to implemnt these into the integral

[rough forge]

ok...

,, \int_0^2 4u^2 \sqrt{u^3+1} : \dd u

[jolly parrot]

bacc (unhelpful)

[rough forge]

We know what u^3+1 is and du

[deft quiver]

yes

i understand how to get the differential du but where does that come into play

[rough forge]

,, \int_0^2 4u^2 \sqrt{\textcolor{cyan}{u^3+1}} : \textcolor{green}{\dd u} = \int_{x_1}^{x_2} 4u^2 \sqrt{\textcolor{cyan}{x}} \cdot \textcolor{green}{\frac{1}{3u^2} : \dd x}

[jolly parrot]

bacc (unhelpful)

[deft quiver]

ohhhh

i see

the color coding works haha

now wouldnt you put 4 outside the integral because its a constant?

[rough forge]

and the 1/3

[deft quiver]

so 4/3

[rough forge]

x_1 and x_2 denote the new bounds for our integral

[rough forge]

yes

u^2 cancels

[deft quiver]

ok imma write this stuff down

[rough forge]

Now either you figure out the new bounds or you "keep" the old ones, but then after integration you must resubstitute

[deft quiver]

I think i solve using the bounds given

[rough forge]

I wouldn't

The new bounds are easy to find

You use the substitution equation

x = u³+1

Now lower bound was u=0

so new lower bound is x = 0³+1 = 1

old upper bound was u=2

so new upper bound is x = 2³+1 = 8+1 = 9

[jolly parrot]

bacc (unhelpful)

[deft quiver]

hm ok I dont know if I have learned to make new bounds yet but i can run that by with my TA

but thank you

theres one more questions that I was working on and using two different online website to help me find the answer and it was contradictory so I dont know if im on the right track

[rough forge]

ok

[rough forge]

first thing I noticed

[rough forge]

that should have been a +

[deft quiver]

sorry if its really confusing how i was working on it haha

[jolly parrot]

bacc (unhelpful)

[deft quiver]

oh i see

wouldnt i have to move the 3 outside too?

and the 2 ?

from 1/2x^2

[rough forge]

You started with [ \frac{1}{4} \left ( 3 \cdot \int \frac{1}{x} : \dd x + 2 \cdot \int \frac{1}{x^2} : \dd x - \int \frac{1}{x^3} : \dd x \right )]

[jolly parrot]

bacc (unhelpful)

[deft quiver]

oh yes thats right

[deft quiver]

so this is the final integration right and from that i add in the bounds

[rough forge]

ys

[deft quiver]

ok great thank you so muhc?

!

[rough forge]

Have a great day.

[deft quiver]

thanks you too

wait i have one more question, how do you know when to use substitution, does it just depend on what youre working with?

[rough forge]

Whenever your integral looks hard to compute straight away, you wanna simplify it

Substitution is all about making your integral easier to compute

[pearl pond]

@deft quiver Has your question been resolved?

[pearl pond]

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[spiral sage]

P(t) = 7500 + 3000sin((pi*t)/8). How do we find the second time where P(t) = 10000.

[pearl pond]

@spiral sage Has your question been resolved?

[pearl pond]

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[sweet condor]

Let me translate it

Is it the good method for having the good equivalance class ?

z is (x,y) and z1 = (x_1,y_1)

and I'm trying to find all the element of the class (0,1)

[midnight haven]

@sweet condor Nan bg c'est pas bon là

[sweet condor]

Oh coucou :D

Je vois pas alors ce que je dois faire pour trouver les elements

[midnight haven]

Déjà une erreure simple

Quand t'as pris la racine carré des 2 côtés t'as pas mis +-

$\pm$

[jolly parrot]

jan Lapiwin is also jan Niku

[midnight haven]

genre ça

[sweet condor]

La consigne de base c'est "SI R est une relation d'equivalance, que représentent les classses (0,1) (0,0) (1,0) ? Donner une illustration de ces classes dansle plan des réels

[sweet condor]

Comment ?

[midnight haven]

Genre si t'as x^2=2

C'est quoi les 2 solutions?

[sweet condor]

Il a encore 2 solution dans les 2 les equation ?

[sweet condor]

-2 et ou 2

[midnight haven]

-sqrt(2) et sqrt(2) plutôt

[sweet condor]

OH ousp

[midnight haven]

bah là c'est pareil

Si t'as x^2=y^2-1 alors ça te fait 2 solutions:
- x=sqrt(y^2-1)
- x=-sqrt(y^2-1)

[midnight haven]

Ouais, super

[sweet condor]

Ah -x j'ai oublié d'ecire le -

[midnight haven]

Bon, maintenant, le problème principal

[sweet condor]

ou nan

g rien dit

[midnight haven]

Ta solution c'était (sqrt(y^2-1);sqrt(x^2+1))

[sweet condor]

hm hm

[midnight haven]

Donc ton x est défini à partir de y et ton y est défini à partir de x

pas très pratique hein

[sweet condor]

en effet j'ai pas idée...

je me suis basé sur l'explication d'une vidéo

Sinon côté graphique ca va pour l'instant (il faudra que je mettent la verison negative aussi)

[midnight haven]

En fait maintenant que t'as la relation exacte entre x et y vaut mieux choisir une seule des 2 variables et définir l'une selon l'autre

Je sais pas si cette phrase est claire

[sweet condor]

Hm

Tu veux que je garde x

[midnight haven]

Oui, ce serait une bonne idée

[sweet condor]

mais que y je le change pour avoir que des x

[midnight haven]

oui

[sweet condor]

dernière question

[midnight haven]

Tu pourrais aussi faire l'inverse mais je pense que ce sera plus facile de toute définir en terme de x

[sweet condor]

On est pas sensé avoir un couple a la fin ?

[midnight haven]

euh si

bah c'est ce que t'as eu non?

(truc;autre truc)

[sweet condor]

Oui mais je note comme tu as fait ?

[midnight haven]

grossomodo oui

@sweet condor Bref, donc si tu fais ce que tu viens de dire, t'obtiens quoi?

[sweet condor]

let me write it down

[midnight haven]

Ok

Bon techniquement y'a un dernier truc auquel on doit s'assurer

[sweet condor]

hm ?

[midnight haven]

Faut vérifier que sqrt(x^2+1) et -sqrt(x^2+1) soient tous les deux dans R

Parce que, si par exemple on avait plutôt (x;sqrt(x+2)) et que on choisissait x=-3 alors en y on aurait sqrt(-3+2)=sqrt(-1), ce qui n'est pas dans R

[sweet condor]

pour x = 0 on a sqrt(1) et -sqrt(1)

x^2 est toujours positive

Quand tu fait lequation du 2nd degré avec tu obtiendra un delta negative

le signe de x^2 + 1 est donc positif sur R

[midnight haven]

Exactement

[sweet condor]

On conclus que sqrt(x^2 +1) et -sqrt(x^2+1) est dans R

[sweet condor]

yess

[midnight haven]

Donc tu peux dire "pour tout x dans R" (avec la notation que vous utilisez)

sans problème

[sweet condor]

Vbar x € R

nice

[midnight haven]

@sweet condor D'autres questions?

[sweet condor]

Oui

Mais j'ai envie de finir de régier cette question

Est-ce que je peux liberer le channel et te demander en pv quand je bloque encore ?

[midnight haven]

Oui

Pour ça faut envoyer la commande .close

[sweet condor]

.close

[pearl pond]

Channel closed

Closed by @sweet condor

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Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[midnight haven]

what have you tried

[compact ridge]

this person keeps reopening and closing their q

don't help them

[oak quiver]

mods?

[compact ridge]

I DMed ModMail

[unkempt yacht]

please stop closing and opening new channels

[midnight haven]

I tried to find the an part

So I kinda tried just Geometric and Arithmetic

which did not work

its arithemtic

and it's like a mumbo jumbo of confusion

[oak quiver]

nope harmonic

[midnight haven]

the an = a1 (n - 1)d?

[oak quiver]

its an = 1/(a1 + (n - 1)d)

[oblique schooner]

why are you opening and closing channels

[oak quiver]

all the terms of arithmetic have been reciprocated

[oblique schooner]

you can reopen the same one if you need to, and if you don't stop wasting channels

[midnight haven]

<@&268886789983436800> I do not feel comfortable around Ren. If I address it I know things will get worst so I kept leaving until he stops following through every channel I made.

[compact ridge]

you can DM @spare sparrow if you feel uncomfortable around them

[midnight haven]

1/? but

[oak quiver]

that is arithmatic

this is harmonic

[oak quiver]

^

[midnight haven]

yes and he said arithmetic

[oak quiver]

its not arithmatic bro

[oblique schooner]

If you have an actual problem for a specific reason then message modmail, even if you do you can block them and I don't see how that justifies opening multiple channels when its not stopping anyone from viewing the new one

[midnight haven]

this is getting confusing which one is it?

[oak quiver]

harmonic

[midnight haven]

Okay

[oak quiver]

^

[midnight haven]

n / [1/x1 + 1/x2 + 1/x3 + ... + 1/xn]?

[oak quiver]

what will be a1?

no no

[oak quiver]

harmonic mean lmao

we are talking about harmonic progression/series/etc

[midnight haven]

oh

soery i was distrased

[oak quiver]

if arithmatic is 2, 4, 6, 8 ....
harmonic is 1/2, 1/4, 1/6, 1/8, ...

[midnight haven]

yeah its not arithemtic

its harmonic as he said

[oak quiver]

can i say i told you so?

[midnight haven]

yea

sure

idc

its an = 1/(a1 + (n - 1)d)
an = 1/(1/2 + (n - 1)d)

[oak quiver]

what will be a1?

[midnight haven]

yes

ong you've opened 4 help channels

correct

1/4

[oak quiver]

a1 is not 1/2

a1 is 2

[midnight haven]

he said correct

CMONNN

bro

[oak quiver]

lmao

[midnight haven]

1/2?

how can you like get simple formula where you have to substiture 1 single term wrong

a1 = 1/2

i just assumed it was eight

[oak quiver]

nopeee

[midnight haven]

right

[oak quiver]

a1 = 2

broo

[midnight haven]

its 2

bcz

1/1/2

=>

[oak quiver]

yeah

[midnight haven]

1* 2

So.. no more fraction?

=2

Okay..

[oak quiver]

yupp

[midnight haven]

So if they ask a2 for that question I'd say 4?

yes

ok

[oak quiver]

see its like this 1/a1 + 1/a2 + 1/a3 + ...... = 1/2 + 1/4 + 1/6 + .....

so a1 = 2

[midnight haven]

So again.
an = 1/(2 + (n - 1)d)

[oak quiver]

yess

[midnight haven]

yes

[oak quiver]

d is?

[midnight haven]

2?

no

1/2?

i mean

wait

[midnight haven]

yes

[oak quiver]

yes

so an will be?

[midnight haven]

ok whatever i forgot those things

[oak quiver]

np

[midnight haven]

an = 1/(2 + (n - 1)2)

[oak quiver]

yess

simplify this

[midnight haven]

Lemme solve it then

Final anser: 1/2n + 4

[oak quiver]

nope

close tho

? @midnight haven

[midnight haven]

open brackets on (n-1)2

then something will simplidy

fy*

Idk how

[oblique schooner]

You've already been muted before for public drama, stop dragging things into public and breaking server rules or being disruptive as a result. I can't dm you this either because you have them turned off.

If you need to, just block and ignore anyone you don't like, and if there's a serious enough thing they've done that would be banworthy then just let modmail know. There's no reason for anything in between.

[midnight haven]

It's kinda been how many mins since it just didn't discuss it

I kinda think Your making a fuss about it now considering it's already done

[oblique schooner]

I'm warning you because you'll be banned if you repeat things like this

[midnight haven]

You could have warned me during that discussion

[oblique schooner]

I checked your post history and tried to DM you first

[midnight haven]

How

Like

All I did was
1/(2 + (n - 1)2
1/(2 + 2n - 2)
1/(2n)

[oak quiver]

^

[oak quiver]

this is correct

[midnight haven]

oops

[oak quiver]

lol

i guess you are done then

gl

bye

[midnight haven]

Bye

@oak quiver

1/2
∑ 1/(2n)
n = 1/12

?

[oak quiver]

limits on n are wrong

[midnight haven]

oh

[oak quiver]

rest is good

[midnight haven]

n = 0?

[midnight haven]

@oak quiver

[oak quiver]

nope

do you remember how to find the limits?

[midnight haven]

...

All I know is a1 and last a

:3

so 1/2 and 1/12

[oak quiver]

hmmm

you are supposed to do this

an = 1/2
so you will get n

[oak quiver]

this is the lower limit

then an = 1/12
this will be upper limit

[midnight haven]

Oh

So n = 1/2?

[oak quiver]

nopee

[midnight haven]

Hmm

[oak quiver]

^

[midnight haven]

n = 1/12 lower limit

??

1/2 upper limit?

[oak quiver]

noo

n in a natural number lol

[midnight haven]

n = 1/2?

hmm..

n = 1/4?

[oak quiver]

what is an?

[midnight haven]

nth term

n = 1?

n = 7??

n = 6??

@oak quiver

[oak quiver]

yes

[oak quiver]

yes

nice

[midnight haven]

so answer is..

n = 6?

[oak quiver]

limits are that

[midnight haven]

soo

1/12 upper limit

but isn't the upper limit 1/14?

and the lower limit n = 7

??

@oak quiver

[oak quiver]

ummmmm

to get the limits

tell me what the first term is

[midnight haven]

1/2

[oak quiver]

now what is an?

[midnight haven]

1

[oak quiver]

?

[midnight haven]

wsit

[oak quiver]

wsit?

nvm got it

[midnight haven]

1/(2n)

[oak quiver]

yeah

and pls talk in more than 1 word

equate an and a1

[midnight haven]

1/(2n)..... and... 1/2

equals....

Uhhhh

1/(2n) + 1/2

[oak quiver]

equate

not add

[midnight haven]

....

1/(2n) = 1/2

[oak quiver]

yes

n equals?

?

[midnight haven]

...

4/2?

n = 2

no.

[oak quiver]

silly error lol

[midnight haven]

0/2

n = 0/2

[oak quiver]

howww?

that isnt correct

[midnight haven]

....

[oak quiver]

solve for n

n isnt 0/2

hint: ||cross multiply||

[midnight haven]

I did??

1/2 - 1/2

oh 1

[oak quiver]

yeah

now what is the last term?

[midnight haven]

1/14

@oak quiver

<@&286206848099549185>

[pseudo oxide]

are you still doing this?

...?

okay are you just not gonna talk

[round patio]

https://youtu.be/l-6uEtTBH7g?feature=shared

You might wanna see this

[oak quiver]

thnx bro

[midnight haven]

Hey

Sooo

[oak quiver]

sorry

[midnight haven]

its fine

[oak quiver]

yes

[midnight haven]

So..

[oak quiver]

so to find the upper limit of n

equate last term with an

[midnight haven]

1/(2n) = 1/14?

[oak quiver]

yeahh

solve for n

[midnight haven]

n = 12/14?

[oak quiver]

ummm

no

[midnight haven]

...

[oak quiver]

^

[midnight haven]

I DID

n = -12/14?

[oak quiver]

ye

[oak quiver]

nopee

1/2n = 1/14
2n = 14

do you see how?

[midnight haven]

HUH??

[oak quiver]

cross multiply

[midnight haven]

1/2n = 1/14
n = 1/14 - 1/2..

[oak quiver]

that isnt cross multiplication lol

[midnight haven]

To get n...

I need to divide both sides by 1/2...

[drowsy bobcat]

What are you guys talking about

[midnight haven]

Ohhhh

[oak quiver]

you are subtracting lol

not dividing

[midnight haven]

okay-

[oak quiver]

yeah but you would get 1/n not n

cross multiplication better

[midnight haven]

so that's it?

[oak quiver]

yup

[midnight haven]

No... n = 14/2

No... divide both sides

No.. nothing?

[oak quiver]

simplify lol

[midnight haven]

So that's already n..

2n = 14

[oak quiver]

are you in disbelief that you did the question?

lmao

[oak quiver]

yeah so what is n?

[midnight haven]

IM DISBELIEF

I FEEL LIKE IM NOT SUPPOSE TO BELIEVE PEMDAS ANYMORE

THIS IS CONFUSING

[oak quiver]

PEMDAS?

BODMAS?

[midnight haven]

NO MORE DIVIDE BOTH SIDES

NO MORE GETTING N

NO MORE N = SOMETHING SOMETHING NUMBERS

AS IN GONE??

OUT OF THIS TOPIC???

NOT MORE???

[oak quiver]

?

[midnight haven]

LIKE

[oak quiver]

im super confused

[midnight haven]

I JUST DID DIVIDE BOTH SIDES

DID LIKE n = 14/2

BECAUSE THAT WAS LITERALLY TAUGHT LIKE THAT

MY WHOLE ENTIRE LIFE

[oak quiver]

yeah that is all correct

[midnight haven]

IM LIKE SHOCK

THAT'S IT??

[oak quiver]

ohh lol

[midnight haven]

NO MORE CONFUSING THINGS NO MORE STEPS??

[oak quiver]

simplify this pls

[midnight haven]

n = 7

[oak quiver]

yess

so the limits are?

(pls dont say 1/2)

[midnight haven]

1/14.. upper limit..

n = 7 lower limit..

[oak quiver]

^

[midnight haven]

2n = 14 ??

[oak quiver]

^

limits are 1 and 7

n cant be a fraction

n being a fraction doesnt make any sense

[midnight haven]

...

n = 1...?

[oak quiver]

yeah

from an = first term

we get n=1

[midnight haven]

and...

1/14 upper limit..

[oak quiver]

istg

[midnight haven]

...

[oak quiver]

this is the limit

1/14 is just the term

[midnight haven]

in what... limit...

lower??

upper??

middle??

[oak quiver]

upper ofc

[midnight haven]

Okay...

then..

were done??

[oak quiver]

do you know what limits is?

[midnight haven]

no lower limit..

Okay

[oak quiver]

?

[midnight haven]

n = 7
∑ 1/(2n)

[oak quiver]

1 and 10 are the limits in this sigma

[midnight haven]

...

[oak quiver]

lower limit?

[midnight haven]

...

n = 1

[oak quiver]

PLS TALK IN MORE THAN 1 WORD

[midnight haven]

IDK

2???

0???

[oak quiver]

wtf is 2?

more than 1 word pls

[midnight haven]

0!!

[oak quiver]

MORE THAN 1 WORD

[midnight haven]

2???

[oak quiver]

MORE THAN1 WORD

[midnight haven]

3??

[oak quiver]

ISTG SAY SOME SENTENCES

[midnight haven]

THREE

[oak quiver]

LIKE LOWER LIMIT IS SOMETHING

NOT SOME RANDOM NUMBERS

[midnight haven]

THEN SOMETHING

THE LOWER LIMIT = SOMETHING

[oak quiver]

WHAT IS THA SOMETHING?

[midnight haven]

it's something

[oak quiver]

nobody can help you

bye

gl

[midnight haven]

IDK

Like

IT'S MORE THAN 1

LESS THAN 1

THEN WHAT??

1.5?

0.5??

@oak quiver

IDK WHAT IS MORE THAN 1 AND LESS THAN 1

0 AND 2 IS THE CLOSEST GUESS I CAN DO

BUT NO

IT'S WRONG

IDK WHAT IM GUESSING HERE

THE CLOSEST GUESS I CAN MAKE OUT OFF THIS IS 2

MORE THAN 1

ong..

Bro saying more than 1

I answer 2

and still wrong

what a jerk

<@&286206848099549185> Help

[frozen lantern]

this?

!status

[pearl pond]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[urban cove]

hai

[midnight haven]

yes..

This guy @oak quiver kept saying "More than 1"

[urban cove]

are you from which country

[midnight haven]

I answered

2

cause 2 is more than 1

Logical thing

but then It's wrong

Just give me another way to do this

I don't have my limits

?
∑ 1/(2n)
?

[frozen lantern]

what?

[midnight haven]

sigma notation

[frozen lantern]

!status please

[pearl pond]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[oak quiver]

i was saying to speak in more than 1 word

not that the limit is greater than 1

[midnight haven]

oh

Hold on then

lemme get my paraphrase

[oak quiver]

bro an = 1/(2n)
she just needs help with the limits

like n = what to what

[midnight haven]

Let me get my paraphrase

[oak quiver]

you dont know eng?

makes sense lol

[midnight haven]

I'm a FILIPINO

OF COURSE I CAN'T SAY LONG SENTENCES LIKE AMERICANS

[oak quiver]

im not american lol

[midnight haven]

THAT'S WHY IM USING PARAPHRASE

Here

To expand the expression for Sigma Notation, we need to clarify what the summation is representing. Sigma notation, denoted by the Greek letter Σ, is used to represent the sum of a sequence of terms. The general form of a summation in sigma notation is:

[
\sum_{i=a}^{b} f(i)
]

Where:

• (i) is the index of summation.
• (a) is the lower limit of summation.
• (b) is the upper limit of summation.
• (f(i)) is the function or expression being summed.

If you have a specific function (f(i)) and limits for (n), please provide those details. However, if we assume a general case where (n) is the upper limit and we start from (1), the expansion would look like this:

[
\sum_{i=1}^{n} f(i) = f(1) + f(2) + f(3) + \ldots + f(n)
]

For example, if (f(i) = i), then:

[
\sum_{i=1}^{n} i = 1 + 2 + 3 + \ldots + n
]

If you have a specific function or context in mind, please provide that, and I can give a more tailored expansion!

The solution for Sigma Notation is n = 1.

[jolly parrot]

キオ
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[midnight haven]

Is that long enough for you?

[oak quiver]

lmao

what i meant was

instead of saying 1 or 2

say i think the lower limit should be 1

[midnight haven]

n = 1

[oak quiver]

this way i am sure what you are trying to say

[oak quiver]

again

[midnight haven]

OH WAIT PARAPHRASE

[oak quiver]

^

[midnight haven]

WAIT LEMME PARAPHRASE IT

[oak quiver]

is this chatgpt?

[midnight haven]

I am trying to make my sentences longer for you

[oak quiver]

this is good enough for me

[midnight haven]

n = -1?

[round patio]

!img

[pearl pond]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[oak quiver]

USE THIS FORMAT

like

[midnight haven]

lower limit should be 1

[oak quiver]

"i think it should be -1"

[oak quiver]

yeah like that

yes lower limit is 1

[midnight haven]

n = 1

THIS IS LITERALLY MATH WHY IS GRAMMAR IMPORTANT

[oak quiver]

its important so that i understand what you are saying

se all my above messages

they arent 1 words

[midnight haven]

WE ARE DISCUSSING LOWER LIMITS HOW CAN YOU EVEN FORGET THE TOPIC

[oak quiver]

this way you would know exactly what im saying

im not as fast as you

lol

[midnight haven]

Oh

Why didnt you say so?

[oak quiver]

ok so the limits are?

[midnight haven]

1/14 and n = 1

[oak quiver]

(lets say that i had instead said n=? would you hve undertood)

[oak quiver]

pls

[midnight haven]

WAIT NOW YOU KNOW MY PAIN

I AM NOT FAST AT MATH

YOU ARE NOT FAST AT WORDS

AHA!

50 = 50

[oak quiver]

i was being sarcastic lmao

[oak quiver]

use this format for this

[oak quiver]

.

[midnight haven]

i think it should be 1/14 and n = 1

[oak quiver]

also use words like lower limit and upper limit

[midnight haven]

im srsly in a hurry

especially since We have been here since 1 pm

[oak quiver]

srsly?

[midnight haven]

YES.

[oak quiver]

^

[midnight haven]

also use words like lower limit and upper limit

okay

So

Lower limit is n = 1

Upper limit 1/14

[oak quiver]

your upper limit is less than your lower limit

lmao

[midnight haven]

Lower limit is 1/14
Upper limit n = 1

@oak quiver

[south inlet]

no

[midnight haven]

..

[south inlet]

that is not the upper limit nor the lower limit

you seem to have been right the first time saying that the lower limit is 1

but you say you are summing 1/2n from n = 1 to some upper limit that you havent found yet

if your last term is 1/14, you need your upper limit to correspond to 1/14 when you plug it into what youre summing

ie the 1/2n

[midnight haven]

huh?

<@&286206848099549185>

[oak quiver]

how do you find the upper limit?

lower limt = 1 is correct

[midnight haven]

Uhh

last term

[oak quiver]

nope

equate a_n with last term

[midnight haven]

2n = 14?

[oak quiver]

yes

this is the upper limit

the 'n' value corresponding to first term and last term
are the lower and upper limits respectively

[midnight haven]

2n = 14
∑ 1/(2n)
1

[oak quiver]

simplify the 2n=14

[midnight haven]

n = 14/2

[oak quiver]

more simplify

[midnight haven]

n = 7

[oak quiver]

yes

[midnight haven]

so..

n = 7
∑ 1/(2n)
1

[oak quiver]

yes

finally

https://tenor.com/view/rick-roll-nitro-gif-21997352

[midnight haven]

Another questions

Write arithmetic if the sequence is arithmetic. Write geometric if the sequence is
geometric. Write Fibonacci if the sequence is Fibonacci. Write Neither if the sequence is neither arithmetic, geometric, nor Fibonacci.

1. -6, 1, 8, 15, 22
2. 1, 3, 9, 27, 81, 243,
3. 𝑘, 𝑘 + 4, 𝑘 + 8, 𝑘 + 12
4. 9, 12, 21, 33, 54
5. −2, 2, −2, 2
6. 1, 1, 2, 3, 5, …
7. 11, 12, 14, 17, 21

<@&286206848099549185>

[lilac cliff]

Do you know what are the general forms that arithmatic and geometric sequences take?

Or what the fibonacci sequence is

[midnight haven]

Idk fibonacci sequence

[oak quiver]

Fibonacci sequence is:

lets say the first numbers are 1, 2

[midnight haven]

arithmetic..

[oak quiver]

next will be 1+2=3, 3+2=5, 5+3=8 ....

[midnight haven]

OHHHH

It's like series..

[oak quiver]

so the series will be 1, 2, 3, 5 ,8 ....

[midnight haven]

Okay okay

[lilac cliff]

Thats why its called a sequence

[midnight haven]

Ye

[lilac cliff]

Can you write a general form for it tho?

[oak quiver]

so the first one is?

[oak quiver]

nope

[midnight haven]

arithmetic

[oak quiver]

it can be using funcions f(n) = f(n-1) + f(n-2) but not sigma

[oak quiver]

then

[lilac cliff]

a_n=a_(n-1)+a_(n-2) for n>2

[oak quiver]

^

[midnight haven]

geometric

Number 2

[oak quiver]

yes

then?

Write arithmetic if the sequence is arithmetic. Write geometric if the sequence is
geometric. Write Fibonacci if the sequence is Fibonacci. Write Neither if the sequence is neither arithmetic, geometric, nor Fibonacci.

1. -6, 1, 8, 15, 22
2. 1, 3, 9, 27, 81, 243,
3. 𝑘, 𝑘 + 4, 𝑘 + 8, 𝑘 + 12
4. 9, 12, 21, 33, 54
5. −2, 2, −2, 2
6. 1, 1, 2, 3, 5, …
7. 11, 12, 14, 17, 21

im gonna recommend say it like this

number 2 is geometric

[midnight haven]

Okay

Number 2. Fibonaci?-

[oak quiver]

its correct

[midnight haven]

SORRY

[oak quiver]

number 3?

[midnight haven]

Number 3!!
Fibonaci

Misclick

[oak quiver]

nope

[midnight haven]

Oh

Arithmetic

Number 3 is arithmetic

[oak quiver]

dont guess lmoa

tell me why?

[midnight haven]

I'm not literally guessing

[oak quiver]

?

[lilac cliff]

Fibonacci is basically the sum of the 2 previous terms in a sequence

[midnight haven]

I know it's arithmetic because the meaning of it revolves around addition

[oak quiver]

its arithmatic because the diff of adjacent terms is constant

what does geometric mean?

[midnight haven]

It revolves around multiplication

[oak quiver]

in this form ^

[midnight haven]

I don't speak math language...

[oak quiver]

the ratio/division is constant

lol

[lilac cliff]

Ngl fair point

[midnight haven]

So number 3, Arithmetic

[oak quiver]

yess

4?

[midnight haven]

Fibonacci

[oak quiver]

why?

[midnight haven]

...

Because,,

it..

[lilac cliff]

Looks cool

[oak quiver]

!da2a

[midnight haven]

looks like it..

[pearl pond]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[oak quiver]

fair enogh

5?

[midnight haven]

Neither?

[oak quiver]

nope

[midnight haven]

Geometric

[oak quiver]

yess

6?

[lilac cliff]

For 4 the reason its fibonacci because starting from the 3rd term its the sum of the previous two terms, and for the 4th its also the sum of the previous 2 terms and goes like that

[midnight haven]

Fibonacci

[oak quiver]

yes

7?

[midnight haven]

Arithmetic

[oak quiver]

how?

[lilac cliff]

Lets assume x=theta

[midnight haven]

11 + 1 = 12 + 2 = 14 + 3 = 17 + 4 = 21

[lilac cliff]

Exactly xdddd

[oak quiver]

but the diff isnt constant

[midnight haven]

yes it is

[oak quiver]

^

first its 1

then 2 then 3

its increasing

thats isnt an AP

[midnight haven]

well it's not a fibonnaci because the sequence doesn't add up to the 3rd term

[lilac cliff]

You cant generalise it in the form of a_n=a_1+(n-1)r with r being a constant difference

[midnight haven]

It's not geometric because it doesn't multiply to the 2nd term

So it's arithmetic

Oh wait..

[lilac cliff]

Thats correct but that doesnt mean its arithmetic

[midnight haven]

It's not arithmetic because the common difference is not constant neither..

[lilac cliff]

Mhm

[midnight haven]

Neither

[lilac cliff]

Soooo

[oak quiver]

yess

now if you have more doubts then close this and open another

byee

[lilac cliff]

Bye wumpus man

[oak quiver]

it was for her but ok?

[midnight haven]

.close

[pearl pond]

Channel closed

Closed by @languid nexus

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sharp pewter]

Hello! I would need some help solving this

Using geometric sums

I understand from that our first invested capital will be compounded 59 times, since the last investment of 600 wont be compounded.

[versed ledge]

Its geometric sum or compound interest question?

[sharp pewter]

Geometric sum

Both?

r^k *

[versed ledge]

Yeah he is investing every month, compound interest has just one capital at beginning of investment

[sharp pewter]

what?

[versed ledge]

Nvm, I am not aware of such questions sorry

[sharp pewter]

Oh okey np

Im just wondering since the 600 last month wont be compounded, will it be like this ?

So first payment will be compounded 59 times, second payment will be compounded 58 times and so on..

ahh

I dont understand someone help me D:

[sharp pewter]

.

[pearl pond]

@sharp pewter Has your question been resolved?

[sharp pewter]

Alr I solved the other question.

But for this, where the function is increasing or decreasing, do i just do the derivative and find the critical points and then a sign diagram ?

[midnight haven]

yes

[pearl pond]

@sharp pewter Has your question been resolved?

[sharp pewter]

.close

[pearl pond]

Channel closed

Closed by @sharp pewter

Use .reopen if this was a mistake.

Channel closed

Closed by @sharp pewter

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gusty moss]

please help em

[pearl pond]

@gusty moss Has your question been resolved?

[gusty moss]

<@&286206848099549185>

im desperate

[gusty moss]

😭

[pearl pond]

@gusty moss Has your question been resolved?

[burnt narwhal]

who is gauss

oh ok i knew him

[gusty moss]

u knew him??? damn

how old are u

200?

[burnt narwhal]

hhhhhh

hes my spiritual uncle

[gusty moss]

lmfao

<@&286206848099549185>

[gusty moss]

<@&286206848099549185>

is htis problem really that hard

[plush bramble]

Maybe!

Did you set up a matrix yet

[gusty moss]

yeah but

i get a cubic

and idk where to go

[plush bramble]

Show all your work

[gusty moss]

its sending

there

the . on top of the 1 is dust its not i

[plush bramble]

Your matrix should have a, b, and c

f(-2) = 4a -2b +c = k

[gusty moss]

oh i got too lazy to label it

the first collumn is a

so on

[plush bramble]

Doesn't look like you finished reducing yet

Also because you left out a, b, c that messed up your row reducing steps

[gusty moss]

hold up

should i restart then

[gusty moss]

did i?

i thought the arithemtic was right

[plush bramble]

Restart with the a, b, c in tact and see

[gusty moss]

ok

@plush bramble

is this right

[plush bramble]

No

[plush bramble]

.

[gusty moss]

i dont get the point of this

why do we need a b c?

😐 i dont understand why

[gusty moss]

fuck

[pearl pond]

@gusty moss Has your question been resolved?

[gusty moss]

.close

[pearl pond]

Channel closed

Closed by @gusty moss

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pine wadi]

i'm trying to understand how to demonstrate the truth of a limit, so I was looking on this website and the first step of the demonstration is the following

[pine wadi]

I was wondering why. My theory is that i'm trying to demonstrate that the difference between f(x) and 0 should be very small when x-->2, therefore it should be included in the interval (-epsilon; epsilon) which is arbitrarily small. Is that it?

[spiral pivot]

Yes exactly

[pearl pond]

@pine wadi Has your question been resolved?

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[midnight haven]

can anyone help me figure this out thx!

[pearl pond]

@midnight haven Has your question been resolved?

[midnight haven]

<@&286206848099549185> anyone ???😭 please

.close

[pearl pond]

Channel closed

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[midnight reef]

if X is a compact set, show S is compact

[midnight reef]

A set is compact if it is closed and bounded, that is the definition I have

so proving S is bounded is not too difficult, what is a good way to show S is closed?

[plush bramble]

Is X a subset of R

[manic abyss]

hi

[midnight reef]

it is not stated

I should be guessing it is

[manic abyss]

@midnight reefi rly need help with calculus

[worthy lance]

!occupied

[pearl pond]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[manic abyss]

where should i go?

[manic abyss]

i sent one message and the room got deleted almost instantly

that's a no ig

[plush bramble]

Did you read #❓how-to-get-help

[midnight reef]

read #❓how-to-get-help

[worthy lance]

Stick here #help-25

[plush bramble]

It got moved, not deleted

[manic abyss]

thxxxxxx

[merry carbon]

And make sure you have the occupied channels expanded so you see those which are all read too

[midnight reef]

taking an element $z \in \bar{S}$ implies that for all $\epsilon > 0$, we have $(z - \epsilon, z+\epsilon) \cap S \neq \emptyset$

[jolly parrot]

Halex

[midnight reef]

being that I want to prove $\bar{S} = S$

[jolly parrot]

Halex

[plush bramble]

How do you know z is real number

[midnight reef]

Even if S was a subset of R, can we tell that taking an element in its closure would implie it is a real number?

[plush bramble]

You have to use that X is compact

In R, closed and bounded subsets are equivalent to compact

[midnight reef]

Taking a sequence is better for this case then?

[plush bramble]

Better is just what you're comfortable with

[midnight reef]

Oh, but would it work if I show there's a sequence converging to x + y?

[plush bramble]

Your sequences have that form, so should their limits if they come from X

[midnight reef]

How do I know the closure is not empty?

Well, the set S itself is not empty and S is contained in its closure

[midnight reef]

but I showed x+y is in the closure of S