Sumattion
#simple ig
storm hedge
woeful plumeBOT
Sumattion
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storm hedge
both problems
hot thunder
English, please?
storm hedge
ik the second one i can do it using t1/ 1 - 1/7 but when it is 2/7 instead of 1/7 it crashed me
hot thunder
...I gathered that much.
storm hedge
;-;
hot thunder
We don't actually even need to find the total sum.
storm hedge
nope
hot thunder
So if we reduce the terms mod 1000, what do we get?
hot thunder
...it means we subtract all whole multiples of 1000 from the number.
hot thunder
...okay, but we don't need one here...
hot thunder
im rlly bad at summation formulas
This isn't a summation formula. This is literally a completely different mathematical concept that we're using to simplify the summation problem by ignoring all the parts of it we don't care about.
storm hedge
7
storm hedge
there are no
hot thunder
So then it just stays 7. What about 77?
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77
hot thunder
777?
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777
hot thunder
7777?
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777
hot thunder
...no.
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what
hot thunder
What's the integer part of 7777/1000?
hot thunder
...the part... before the decimal...
hot thunder
teacher just taught methods to get this fast as possible
Well I teach you to understand what you're doing and why.
storm hedge
Well *I* teach you to *understand* what you're doing and why.
theres the teacher that teaches me probabilities with logic and the teacher that teaches me probabilities using combinatorics
777
storm hedge
777
hot thunder
Right. Every term greater than 777 reduces to 777 mod 1000. Which is why that's useful for us, because if all we need to know are the last three digits, then we can literally throw away all the other parts of the numbers.
storm hedge
the idea is get the easiest way to solve this bc in the exam i have a timer
hot thunder
...yes, and when you understand this method, it will be by far the easiest possible way to solve this specific kind of problem.
storm hedge
but im not understanding nothing bc i have to translate whole time ur sentences
jsvv bc jwjensn
hot thunder
Okay. From the top.
storm hedge
but np
hot thunder
We only care about the last three digits, right?
hot thunder
No.
hot thunder
We only care about the last three digits, right?
storm hedge
yes
hot thunder
Is it possible for the fourth digit to affect those three?
storm hedge
nope
hot thunder
So we can literally throw it away and forget it exists. That's what reducing modulo 1000 is.
storm hedge
777+
77
7?
hot thunder
No.
storm hedge
7.40 + 7.38+ 7.36
hot thunder
How does that even make sense in your head?
odd prism
wouldnt it be preferrable to first find the sum and then consider it congruent modulo 1000?
hot thunder
Stop skipping to the end.
storm hedge
😭
hot thunder
wouldnt it be preferrable to first find the sum and then consider it congruent m...
I really don't see how. Then we end up adding up literally 37 digits we don't care about.
hot thunder
So just be patient and let me explain.
storm hedge
oki doki
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yep
hot thunder
We also know that 7777 and 77777 reduce to 777, right?
storm hedge
yep
hot thunder
We can infer (and also prove, but I don't want to strain your attention span that much) that every term greater than 777 reduces to 777 mod 1000.
storm hedge
yes ig
hot thunder
Would it help if I proved it?
storm hedge
nope
hot thunder
Okay.
hot thunder
...it would be an algebraic proof.
storm hedge
skip
hot thunder
Okay.
So then every term greater than 777 reduces to 777. How many 777s does that give us?
hot thunder
Why?
hot thunder
Stop guessing.
hot thunder
Be patient.
storm hedge
im trynna understand but u using terms in english that i never heard in spanish xd
hot thunder
If you think you know, explain why you think you know. If you don't have a reason to think you know, just say you don't know.
storm hedge
i domt know
hot thunder
im trynna understand but u using terms in english that i never heard in spanish ...
I understand that, and I'm sympathetic, but I don't see how randomly guessing helps anything.
storm hedge
continue
hot thunder
Okay.
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im not guessing anymore
hot thunder
So how many terms total do we have?
storm hedge
i dont know
hot thunder
It says so in the question.
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222
hot thunder
Where does it say 222 in the question?
storm hedge
im getting confused
storm hedge
So then every term greater than 777 reduces to 777. How many 777s does that give...
7
?
hot thunder
Read the question. The question says how many terms we have.
storm hedge
40
storm hedge
36?
hot thunder
Explain.
hot thunder
...this doesn't tell me anything. It starts with 7 = 5.
hot thunder
...is 7 less than 777?
storm hedge
ywp
hot thunder
So that's one. Is 77 less than 777?
storm hedge
less is - isnt
hot thunder
less is - isnt
No.
storm hedge
yes
hot thunder
...wait.
hot thunder
less is - isnt
...maybe? This isn't expressed clearly.
hot thunder
less is like 6 is less than 7
...yes, 6 is less than 7.
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8<9
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nope
hot thunder
Is 7777 < 777?
storm hedge
nope
hot thunder
Is any term after that less than 777?
hot thunder
So then how many terms did we count - this is literally counting - that were less than 777?
storm hedge
778
hot thunder
Are you messing with me?
hot thunder
That's... not better.
hot thunder
Literally every time I ask you for a number, even after I've gone into excruciating detail all but telling you what the number should be, you guess something off by an order of magnitude.
storm hedge
numbers less than 777 = 776
hot thunder
Terms less than 777.
hot thunder
And how many terms total?
hot thunder
...problem tells you...
storm hedge
ah 40
hot thunder
So then the number of terms that reduce to 777 is what?
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2
hot thunder
...no, that's the number of terms that don't.
hot thunder
Yes.
So the three digit number we want is the last three digits of the number 7 + 77 + 38 * 777.
storm hedge
so
hot thunder
...so now is the calculator step.
hot thunder
...I dunno, maybe you should reask in Spanish?
Because I don't feel like I really helped you that much.
storm hedge
gonna take all steps after
hot thunder
I don't really know what that means.
storm hedge
when i get in my academy ill tell my teacher to solve this, so hes gonna solve this with the easiest way, and ill compare the easiest way with all things u told me to do
i fee like a kid jsbxksje
when my teacher solve this using the easiest way ill send u this
hot thunder
I don't think he can use a method easier than this. This was only difficult because you were unfamiliar with it and because there was a language barrier
storm hedge
I don't think he can use a method easier than this. This was only difficult beca...
there would be
i mean
hot thunder
Also all the guessing didn't help.
storm hedge
what u use for this
100x1 + 99x2 + 98x3… 1x100
sumattion
this sigma symbol
teacher told us to do (100)(100+1)(100+2) / 6
hot thunder
$\sum_{n = 1}^{100} n*(101-n)$
storm hedge
instead of this
storm hedge
teacher told us to do (100)(100+1)(100+2) / 6
we do this
normal glacierBOT
Techie Literate
hot thunder
You asked for "this sigma symbol". I thought you meant you wanted me to express it in sigma notation.
storm hedge
teacher told us to do (100)(100+1)(100+2) / 6
this formula makes that more easy
hot thunder
No it doesn't, not if you don't understand why it works.
Because if you know 100 formulas but you don't actually understand what any of them mean, you're just going to guess which one to apply, and you'll have a 1% chance of guessing right.
And that's not even accounting for if the one you need isn't one you know, which you wouldn't be able to recognize, or if you do guess the correct formula but then misapply it.
hot thunder
...what?
storm hedge
its supposed that is right
wait
it sending
7.40 = _28_0
7.39 = 273 + 28 = _30_1
7.38 = 266 + 30 = _29_6
but we dont care that 29 so: 0+1+6=7
hot thunder
Where are these decimals coming from?
hot thunder
Okay.
storm hedge
is that way easiest
hot thunder
In that case, you're correct that everything I just explained to you is equivalent to 40*7 + 39*70 + 38*700.
storm hedge
ah
hot thunder
But again, it's important to grasp the why.
storm hedge
yep but not in this case
i mean
this question is from an exam
im not going to prove the why in an exam
i just need to solve the problems fast as possible
hot thunder
im not going to prove the why in an exam
That doesn't mean you don't need to understand it.
storm hedge
That doesn't mean you don't need to understand it.
mayb after i pass the exam
just three hours to solve 100 questions
hot thunder
mayb after i pass the exam
That is literally completely backwards. The exam is supposed to test your understanding.
hot thunder
...that doesn't change what I said.
storm hedge
theres ppl that just memorize answers
and can join
exam pass ppl that has the best score
doesnt matter the solution
hot thunder
Yes, and those people burn out during the actual courses because they don't understand the things on the entry exam and so they can't understand the things in the classes.
hot thunder
What are you going for?
hot thunder
Okay.
hot thunder
It's still a good idea to understand math in that case, depending on your field.
storm hedge
months ago i tried to prove hippocrates moons
hot thunder
I don't even know what that is. I think maybe you mistranslated.
storm hedge
my teacher told me to focus joining university
after that i can try to know the why of all
storm hedge
I don't even know what that is. I think maybe you mistranslated.
this 2 triangles with the circles
that says the area of the triangles is the same to the area of the moons