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anonymous
 5 years ago
Absolute Conversion...
Sum(1)^n/(5+n)
Which test do I use?
anonymous
 5 years ago
Absolute Conversion... Sum(1)^n/(5+n) Which test do I use?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\sum_{n=1}^{\infty} (1)^{n}/(5+n)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think I got it... I just forgot that I should use the conversion rules: Bn+1 < Bn and lim (n>inf) =0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the conversion rules? hmm, so what'd you get as the answer?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well, I got conditionally convergent. But it seems that that isnt quite right. Could you go through the steps for me?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first of all don't confuse conversion and convergence i assume it's convergence you've been talking about the whole time, right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0absolute convergence means that the absolute value converges. so you can deal with the series 1/(5+n)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0did you do any tests?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I 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
 5 years ago
Best ResponseYou've already chosen the best response.0do you know the ratio test, the root test, and the integral test?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, but I have trouble deciding which to use.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well you just have to start trying things, don't be lazy

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The 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
 5 years ago
Best ResponseYou've already chosen the best response.0well, you've made a mistake if the tests are telling you different things :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0OCT, 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
 5 years ago
Best ResponseYou've already chosen the best response.0i 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
 5 years ago
Best ResponseYou've already chosen the best response.0Absolute convergent, conditionally convergent, or divergent is the exact wording

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, 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
 5 years ago
Best ResponseYou've already chosen the best response.0so 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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