anonymous
  • anonymous
Absolute Conversion... Sum(-1)^n/(5+n) Which test do I use?
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\sum_{n=1}^{\infty} (-1)^{n}/(5+n)\]
anonymous
  • anonymous
(-1)^n / n+5
anonymous
  • anonymous
hey, how's it going?

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anonymous
  • anonymous
I think I got it... I just forgot that I should use the conversion rules: Bn+1 < Bn and lim (n->inf) =0
anonymous
  • anonymous
the conversion rules? hmm, so what'd you get as the answer?
anonymous
  • anonymous
well, I got conditionally convergent. But it seems that that isnt quite right. Could you go through the steps for me?
anonymous
  • anonymous
first of all don't confuse conversion and convergence i assume it's convergence you've been talking about the whole time, right?
anonymous
  • anonymous
hahaha, yeah oops.
anonymous
  • anonymous
absolute convergence means that the absolute value converges. so you can deal with the series 1/(5+n)
anonymous
  • anonymous
did you do any tests?
anonymous
  • anonymous
I did ordinary convergence test. But that doesnt work. because I compared to 1/n, and that's divergent, but 1/n+5 is smaller than that.
anonymous
  • anonymous
do you know the ratio test, the root test, and the integral test?
anonymous
  • anonymous
yeah, but I have trouble deciding which to use.
anonymous
  • anonymous
well you just have to start trying things, don't be lazy
anonymous
  • anonymous
The issue is that when one test tells me that it's convergent, another tells me it's absolute convergent and another says divergent, I get confused. Since a function can be partially convergent etc. I need to sort out which test test what.
anonymous
  • anonymous
well, you've made a mistake if the tests are telling you different things :)
anonymous
  • anonymous
OCT, LCT, Integral, Ratio, Root, Absolute convergence By the way, the convergence rules I was talking about was the alternating series estimation theorem Which do I use first? My process right now is to use the theorem first. then if it's convergent, use one of the above. And for non alternating, just use one of the above what do you say? is there a better way?
anonymous
  • anonymous
i don't know, it doesn't matter that much what order, just start doing tests. do you just have to find out if the series is absolutely convergent?
anonymous
  • anonymous
Absolute convergent, conditionally convergent, or divergent is the exact wording
anonymous
  • anonymous
ok, an alternating series converges if the limit of the last term approaches 0, and the series is monotonically decreasing which means that An >A(n+1)
anonymous
  • anonymous
so if the terms are getting smaller, and the last term is going to 0, then it converges if it's an alternating series, so that part is not that hard

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