Hello, please help me show that this infinite sum converges (I think it does). Which criteria should I use and how?
Hello, please help me show that this infinite sum converges (I think it does). Which criteria should I use and how?
Jonathan Kelly
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Eli Wright
this is trivial.
Each term is decreasing and they are alternating in sign. It has to converge by the pendulum test.
Carson Cruz
Might I add, which is important, that the limit of each term is zero. If they were just decreasing monotonically, but had a lower bound, they wouldn't have to converge.
Jeremiah Nguyen
Isn't that the basic condition for convergence?
Yeah, it's trivial when you can do derivatives without mistakes (somehow the derivative was positive last time I calculated it).
Henry Thomas
>do derivates without mistakes
Okay, you're making a big mistake. When you're doing math not everything is about being rigorous or following the steps.
Just look at the fucking thing. It obviously is constantly decreasing. Use common sense.
Anthony Thompson
to be fair, op did say "i think it does"
the thing is "common fucking sense, bro!" is not sufficient proof in most circles
Anthony Sanchez
evaluate
[math]
\lim_{n\to\infty}\frac{n+1}{n\log\left(n^2+1\right)} = 0
[/math]
so that by the alternating series test it converges
Lucas Carter
Youre a retard. Having a limit be 0 doesnt mean it converges
>What is the harmonic series
Fucking kill yourself you goddamn brainlet
Nathaniel Sanders
I believe the alternating series test will work.
is clearly a brainlet but they stumbled on a partially valid point. To use the alternating series test you need the terms to be eventually decreasing in absolute value.
These terms do decrease in absolute value, but you need to justify that.
Wyatt Brooks
Fucking disgusting brainlet,
quotes the alternating series theorem, the Leibniz criterium.
Thomas Flores
Nothing remotely wrong with what I said
Lincoln Stewart
There exist alternating series whose terms approach zero and diverge.
So there is something wrong with what you said.
The alternating series test I know requires that the terms also be decreasing in absolute value.
William Butler
>tldr;
>help me pass my calc 2 final
>t. brainlet
Aiden King
>Having a limit be 0 doesnt mean it converges
i expressly invoked the ALTERNATING SERIES test to conclude that it converges you mongrel
Thomas Stewart
then you better look up what you're invoking, because you fucked it up.
Juan Lewis
please explain
Jackson Gomez
the terms have to be decreasing in absolute value have a limit of 0 and the sign has to alternate.
You only wrote the part about the alternating signs and the limit of 0 so there is still something to prove (even though it's simple)
Daniel Ortiz
If we have an alternating series
[math] \sum_{n=1}^\infty a_n [/math]
with
[math] a_n + (-1)\cdot a_{n+1} = \dfrac{1} {n} [/math]
then it wouldn't converge. How can we rule out that the above equation has a solution?
Dylan Gomez
The theorem needs the absolute value of the general term [math]| a_n | [/math] to be decreasing, and that it goes to 0.
Tyler Cook
yeah, true, i figured it was clear enough that it is monotonically decreasing
thanks for keeping things real!
Adam Anderson
What's the name of the theorem?
Because it's not evident
[math] a_n + (-1)\cdot a_{n+1} = \dfrac{1} {n} [/math]
is rules out, just from [math] (a_n)_n [/math] being decreasing and going to zero.
Landon James
Camden Diaz
Does the limit go to 0?
Are the positive terms non-increasing?
If yes to both, it converges.
Pay the Fuck attention in class. I hope to god youre not my tutee.