Question

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

Answer 1

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

Answer 2

(-1)^n / n+5

Answer 3

hey, how's it going?

Answer 4

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

Answer 5

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

Answer 6

well, I got conditionally convergent. But it seems that that isnt quite right.

Could you go through the steps for me?

Answer 7

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

Answer 8

hahaha, yeah oops.

Answer 9

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

Answer 10

did you do any tests?

Answer 11

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.

Answer 12

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

Answer 13

yeah, but I have trouble deciding which to use.

Answer 14

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

Answer 15

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.

Answer 16

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

Answer 17

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?

Answer 18

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?

Answer 19

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

Answer 20

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)

Answer 21

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