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

1. anonymous

$\sum_{n=1}^{\infty} (-1)^{n}/(5+n)$

2. anonymous

(-1)^n / n+5

3. anonymous

hey, how's it going?

4. anonymous

I think I got it... I just forgot that I should use the conversion rules: Bn+1 < Bn and lim (n->inf) =0

5. anonymous

the conversion rules? hmm, so what'd you get as the answer?

6. anonymous

well, I got conditionally convergent. But it seems that that isnt quite right. Could you go through the steps for me?

7. anonymous

first of all don't confuse conversion and convergence i assume it's convergence you've been talking about the whole time, right?

8. anonymous

hahaha, yeah oops.

9. anonymous

absolute convergence means that the absolute value converges. so you can deal with the series 1/(5+n)

10. anonymous

did you do any tests?

11. 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.

12. anonymous

do you know the ratio test, the root test, and the integral test?

13. anonymous

yeah, but I have trouble deciding which to use.

14. anonymous

well you just have to start trying things, don't be lazy

15. 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.

16. anonymous

well, you've made a mistake if the tests are telling you different things :)

17. 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?

18. 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?

19. anonymous

Absolute convergent, conditionally convergent, or divergent is the exact wording

20. 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)

21. 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