/sci/ - Science & Math » Thread #13775976

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Anonymous Thu 21 Oct 13:44:15 2021 No.13775976 View Reply Original Report

Quoted By: >>13775987 >>13776017 >>13776025 >>13776609 >>13776632 >>13776652 >>13776709

Someone explain to me what the fuck are series?
I can't understand anything from my calculus course, I'm too much of a brainlet. I'm gonna fail it if I don't learn this stuff
Who is the actual schizophrenic who came up with this stuff? And what's up with all the criteriums? How do you determine if a series is convergent or divergent?

Anonymous

Anonymous Thu 21 Oct 2021 13:48:07 No.13775987 Report

Quoted By: >>13775996 >>13776027

>>13775976
>series
just an infinite sum
>who is the actual schizophrenic who came up with this stuff
his name is not important
>what's up with all the criteriums
what do you mean
>how do you determine if a series is convergent or divergent
jus b urself

Anonymous

Anonymous Thu 21 Oct 2021 13:52:41 No.13775996 Report

Quoted By:

>>13775987
>what do you mean
I think they are called convergence tests in english?

Anonymous

Anonymous Thu 21 Oct 2021 14:05:46 No.13776017 Report

Quoted By: >>13776023

>>13775976
>How do you determine if a series is convergent or divergent
have you tried reading a book about it?

Anonymous

Anonymous Thu 21 Oct 2021 14:08:06 No.13776023 Report

Quoted By:

>>13776017
im doing that now

Anonymous

Anonymous Thu 21 Oct 2021 14:11:31 No.13776025 Report

Quoted By:

>>13775976
series are just infinite sums on god fr fr

Anonymous

Anonymous Thu 21 Oct 2021 14:13:24 No.13776027 Report

Quoted By:

>>13775987
Series don't need to be infinite dumbass

Anonymous

Anonymous Thu 21 Oct 2021 18:24:59 No.13776609 Report

Quoted By:

>>13775976
the series tests are basically just a dialog tree that you use to test convergence. this video covers most of them.You probably also want to learn the comparison test and the limit comparison test too.
https://www.youtube.com/watch?v=0YeON4p0ogw

Anonymous

Anonymous Thu 21 Oct 2021 18:33:28 No.13776632 Report

Quoted By: >>13776661 >>13776786

>>13775976
i can understand having a hard time with shells or whatever but series? this shit is literally counting. 1, 2, 3... etc. if they look like they're "CONVERGING" on a number then they're converging. if they're doing fuck whatever and zigzagging around and up and getting compoundingly bigger they're diverging

Anonymous

Anonymous Thu 21 Oct 2021 18:42:10 No.13776652 Report

Quoted By: >>13776666

>>13775976
do you understand what the limit of a sequence is?

Anonymous

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Anonymous Thu 21 Oct 2021 18:45:36 No.13776661 Report

Quoted By:

>>13776632
how do you do this then

Anonymous

Anonymous Thu 21 Oct 2021 18:46:37 No.13776666 Report

Quoted By:

>>13776652
yes

Anonymous

Anonymous Thu 21 Oct 2021 18:59:18 No.13776709 Report

Quoted By:

>>13775976
Series ar not Infinite sums.
Series are a special case for sequences. For example, image you have a sequence (a).
Now start adding up the terms of a, and make a new sequence out of this, that is:
{a0, a0 + a1, a0 + a1 + a2, ....}
Let's call this sequence (s), obviously s_k = a0 + a1 + ... + ak
Now, if lim(s) exists, that is lim(s) = s, where s is some real or complex number, we say that the series $\sum_{i=0}^{\infty} a_s$ converges, and we write $s = \sum_{i=0}^{\infty} a_s$

Now, important to note, the notion of infinity is really subtle here, consider what it means for a sequence to converge:
A sequence {x} converges to x if and only if for any epsilon > 0 there exists a natural number N such that if n >= N implies that d(x, x_n) < epsilon

In simple terms a sequence converges to some point x if for any distance you can think of, you can find a sequence term even closer than that.

The "infinity" here is in the "we can always guarantee". it's not some vague "do infinite steps and get the result I want" notion.

Hope this helps

Anonymous

Anonymous Thu 21 Oct 2021 19:21:46 No.13776786 Report

Quoted By:

>>13776632
The sequence of 1/x converges to 0
The series of 1/x does not converge

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