Question
For what values of p is this series convergent?
(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!
(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!
Answers
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
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
Thanks, Steve!
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