For what values of p is this series convergent?

Question

(summation from n = 1 to infinity) of ((-1)^(n-1))/(n^(p + 2))

A. p >= -2
B. p =/= -2
C. p > -2
D. for all p
E. p > 0

You have to use the Alternating Series Test.

I've already tried E, and it was wrong. I have one more attempt. I think it's C, but I want to make sure it's correct before I pick it. Thanks!

Answer 1

The p+2 just confuses things. Let q = p+2. Then you have the series

1/1 - 1/2^q + 1/3^q - 1/4^q

The alternating series test says this converges for q>0

That is p > -2

Answer 2

Thanks, Steve!