#I NEED HELP PLZ

264 messages · Page 1 of 1 (latest)

ornate python
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U_0=1

U_{n+1}=(3U_n+1)/(2U_n+4)

W_n=(2_Un-1)/(U_n+1)

Prove that W_n is geomertic

rigid doveBOT
north jolt
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aight buddy i can NOT help u with that😭😭

ornate python
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Please

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Rip

ebon raft
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lol wth

ornate python
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I find no solution for that

north jolt
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Its not that i dont want to, i havent learned that😭😭

ornate python
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Fr

ornate python
north jolt
ebon raft
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nahhhh

ornate python
north jolt
ornate python
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HE CAN'T RESOLVE IT

ebon raft
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???????????

north jolt
ornate python
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IT TRIED HOUR AND HOUR

ornate python
north jolt
ornate python
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French

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France

north jolt
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voillaaa

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in knew it

ornate python
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Mdr

north jolt
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because u said resolve

ornate python
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Aare you french too?

north jolt
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No english guy would add a “re” by misyake

ornate python
ornate python
north jolt
north jolt
ornate python
ornate python
north jolt
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In french you say “ résoudre”

north jolt
ornate python
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Ouais en gros je suis vraiment de la merde

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À cause de ça

north jolt
ornate python
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U_0=1

U_{n+1}=(3U_n+1)/(2U_n+4)

W_n=(2_Un-1)/(U_n+1)

Prove that W_n is geomertic

ornate python
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Et JSP comment faire

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Et je trouve jamais la solution

north jolt
north jolt
ornate python
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Nop

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Aucun

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Tout sur internet est faux

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La réponse est introuvable

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Il a sorti un truc de bz

north jolt
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att jtenvoie un invite vit fais pour un autre serveur de math ptet la bas qqn peut te rep

ornate python
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k

ebon raft
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Pourquoi votre professeur vous a-t-il posé cette question ?

north jolt
ornate python
ornate python
ebon raft
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super lol

ornate python
#

U_0=1

U_{n+1}=(3U_n+1)/(2U_n+4)

W_n=(2_Un-1)/(U_n+1)

Prove that W_n is geomertic

ebon raft
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hahah

ornate python
ebon raft
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je ne peux pas résoudre ça lol

ornate python
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Rip

ebon raft
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Je suis en huitième année.

ornate python
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Ah

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T'as quel âge ?

ebon raft
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treize ans

ornate python
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Mdr

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Tu connais le second deg ?

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Et ce genre de choses?

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Ou pas

ebon raft
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non

ornate python
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k mais c'est trop ez toi tu peux apprendre stv

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C'est le premeir chapitre en premiere

ebon raft
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je préfère le calcul

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👌

ornate python
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Les trucs que tu fais maintenant genre vrmt ça va être une blague au lycée

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Tu vas devoir le faire automatiquement

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C'est 1000 fois plus difficile

ebon raft
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hm

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non probleme

ornate python
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tu verras ce qui t'attend...........

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conseil: travail beaucoup

ebon raft
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uh

ornate python
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C'est un vrai conseil

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Sinon tu vas fortement regretter

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Vrmt

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Tu vas avoir 1000 trucs à faire en un temps

ebon raft
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Désolé, je dois y aller maintenant.

ornate python
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Bref juste travail bcp

ebon raft
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merci

ornate python
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Vas-y

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Adieu

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U_0=1

U_{n+1}=(3U_n+1)/(2U_n+4)

W_n=(2_Un-1)/(U_n+1)

Prove that W_n is geomertic

elder matrix
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geometric series?

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try strong induction for U{n - 1} then prove it for U{n + 1} until you get geometric series

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i think that should suffice in proving it for U{n + 4}

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then use the induction hypotheses until you get a geometric series

raw light
ornate python
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I dont think is that

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U_0=1

U_{n+1}=(3U_n+1)/(2U_n+4)

W_n=(2_Un-1)/(U_n+1)

Prove that W_n is geomertic

silk ore
kindred tulipBOT
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solarunes

1068960809578930256.png
ornate python
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@silk ore yes

silk ore
ornate python
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But i don't understand what he mean

silk ore
ornate python
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No he didn't prove that it's geometric

ornate python
silk ore
# ornate python No he didn't prove that it's geometric

If you do what he said you'll find that it is indeed a geometric sequence.

Think about how this kind of sequence is defined recursively. For any $W_n$, $W_{n+1}$ can be expressed as some constant times $W_n$. So your goal should be to define $W_{n+1}$ in terms of $W_n$ and see if it meets that criterion.

kindred tulipBOT
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solarunes

1068960809578930256.png
ornate python
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Ye?

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So

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But he didn't prove

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how to solve it

silk ore
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How do you do that? By expressing $U_n$ in terms of $W_n$, then using that in the definition of $W_{n+1}$ to get the desired form.

kindred tulipBOT
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solarunes

1068960809578930256.png
silk ore
ornate python
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idon't understand

ornate python
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I understand ntg for real

silk ore
ornate python
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Yep

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Is

Vn= V0 * q**n

silk ore
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Hint: Just divide V_{n+1} by V_n.

ornate python
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Idk

ornate python
silk ore
silk ore
ornate python
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Vn is v0*q

silk ore
ornate python
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E

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Idk

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Is vn+1

silk ore
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Just use the definition with q you used earlier.

ornate python
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But how to find q

silk ore
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V_{n} = V_0 * q^n
V_{n+1} = ...?

ornate python
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Vn*q

silk ore
ornate python
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Vn*q

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Or Vn=Vp*q(n-p)

silk ore
ornate python
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Is Vn*q

silk ore
ornate python
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Nop

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Vn is Vn*q**n

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Vn+1 is Vn*q

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I am wrong?

silk ore
# ornate python Vn+1 is Vn*q

Exactly! Now you just skipped ahead, that's good. Will save us some time.

So what you know now is that any geometric series will follow this pattern:

V_{n+1} = V_n * q

Where q is some constant that doens't change with respect to n.

ornate python
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Ik

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Yes but how'd find q

silk ore
# ornate python

And so, in the context of this problem, if we can show that

$W_{n+1} = W_{n} \cdot q$

for some q, we will have shown that $W_n$ is indeed a geometric sequence.

kindred tulipBOT
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solarunes

1068960809578930256.png
ornate python
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So?

silk ore
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And we know that W_n can be expressed in terms of U_n. And U_{n+1} can also be expressed in terms of U_n.

ornate python
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Yea

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But how to find Q

silk ore
# ornate python But how to find Q

Remember that, in order to prove that there is such a constant factor q at all, we want to express W_{n+1} in terms of W_n. That's the thing we need to do.

ornate python
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Yes

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But first should find the q

silk ore
# ornate python But first should find the q

No! The q will inevitably show up if the sequence ends up being geometric, because that's how geometric series are defined.
We aren't so much interested in the actual value of q, just if W_{n+1}, again, can be written as W_{n} times some constant.
If we can show this, regardless of the actual value of q, we will have proven that W_n is geometric.

ornate python
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But to make It explicit

silk ore
ornate python
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and how?

silk ore
# ornate python and how?

Let's see...

U_{n+1} can be expressed in U_n
W_n can be expressed in U_n

That means that U_n can be expressed in W_n, too. And then so can U_{n+1}.
And because W_n can be expressed in U_n, W_{n+1} can be expressed in U_{n+1}, and then also in W_n because of the above fact.

ornate python
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I understand nothing u are syaing

silk ore
ornate python
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I am dumb too

silk ore
# ornate python But how to find q

No, you're just new to this kind of problem. It's okay. We'll go through it slowly.

You agree with me that U_{n+1} can be expressed in terms of U_n, right? Consulting this picture?

ornate python
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Yea

silk ore
# ornate python Yea

And it seems logical that we could rearrange the second equation to solve for U_n in terms of W_n, yes?

ornate python
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Yes

silk ore
# ornate python Yes

So, by substituting W_n for U_n in the first equation, after solving the second one for U_n, we can also express U_{n+1} in terms of W_n, do you agree?

ornate python
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but how substituting

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Like taking all the equation and put it

silk ore
# ornate python but how substituting

We can solve the second equation for U_n. Then we get some term involving W_n that is equal to U_n. Then we can just take that term and replace all the U_n's in the first equation with it.

ornate python
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yes

silk ore
ornate python
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How?

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...

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Don't write too much i dont understand more fr

silk ore
# ornate python How?

The first equation expresses U_{n+1} in terms of U_n.

Now you've taken the second equation and solved it for U_n in terms of W_n, so you've got something like U_n = f(W_n).

Now you can just replace all the U_n's in the first equation with their f(W_n)'s, to get U_{n+1} in terms of W_n.

ornate python
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Wait like this

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(3(Wn)+1)/(2(Wn)+4)

silk ore
ornate python
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Fr i dont understand ntg

silk ore
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To see if that helps.

ornate python
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Idk

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We can try

silk ore
# ornate python

Maybe it'll make things clearer.

Okay, so step 1: Solve the second equation for U_n. Go ahead.

ornate python
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?

silk ore
# ornate python ?

Look at the graphic I replied to. Those are the 2 equations that you now, from the task. Solve the second one for U_n.

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U_n = ... something with W_n

Just rearrange it.

ornate python
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Where graphic?

silk ore
ornate python
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Idk

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Fr i see ntg

silk ore
ornate python
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Ye

silk ore
ornate python
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What u mean

silk ore
ornate python
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How

silk ore
# ornate python How

You know how to solve a simple equation, right? It's just arithmetic. I'll even do the first step:

$\newline\newline \left(U_{n}+1\right)\cdot W_{n}=\left(U_{n}+1\right)\cdot\frac{2U_{n}-1}{U_{n}+1}$

kindred tulipBOT
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solarunes

1068960809578930256.png
ornate python
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Wu+w=2u²-U+2u-1/u+1

silk ore
ornate python
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E

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W(u+1)=(2u²+u-1)/(u+1) ?

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Wn=2u²+u-1

silk ore
silk ore
# ornate python Wn=2u²+u-1

No. I suggest using pen and paper or typing it into desmos, then rearranging the terms. Just do it properly, not in your head.

ornate python
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Uep

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So i write

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On paper

ornate python
silk ore
# ornate python This?

This is the first step. I multiplied both sides with the denominator of the fraction on the right, to get rid of it.

ornate python
silk ore
ornate python
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Ok

silk ore
ornate python
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Yep

silk ore
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Then let's go. Find U_n.

ornate python
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Ok

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It can't be more simplified

silk ore
ornate python
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Wait 2 secs i gonna try myself a little bit

silk ore
ornate python
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I found It

silk ore
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Great!

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So what is it?

ornate python
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2/5wn

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I just replace Un by Wn+1 and Un+1

silk ore
ornate python
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Yep

silk ore
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Yes exactly. That's the last step.

ornate python
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but it's a hard question fr

silk ore
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Sure is.

ornate python
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Like we have to think about the formula

silk ore
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Can I ask, what grade are you in?

ornate python
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11

silk ore
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Incredible. When I was in high school, all we did was basic integral calculus and a little analytical geometry.

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This one's quite brutal by comparison.

ornate python
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XD where are u from?

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I am from france me

ornate python
silk ore
silk ore
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Either way, I guess that concludes this matter.

ornate python
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Yep I think too

silk ore
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Type .solved to close this thread.

ornate python
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But when we get the idea we can solve them so easily

ornate python
silk ore
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Have a good one!

ornate python
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U too!

#

.solved