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Homework Statement
The sereis sigma[k=1,inf] [(-1)^k/k^p] converges conditionally for
(a) p<1
(b) 0<p<=1
(c) p>1
(d) p=0
(e) None of the above
Homework Equations
The Attempt at a Solution
The answer key said that (b) was the correct answer and I'm having trouble understanding why
sigma[k=1,inf] |(-1)^k/k^p| = sigma[k=1,inf] |1/k^p|
I got rid of the (-1)^k because the absolute value function will always make it positive and k^p will always be positive for k=1 to infinity so I just got ride of the absolute sign all together
sigma[k=1,inf] 1/k^p
I thought determine which values of p makes this series converge I could determine what values of the original series allows the series to converge absolutely
sigma[k=1,inf] 1/k^p
Is a p-series which converge whenever p is greater one by the integral test
I don't see were I'm going wrong thanks for any help