For what values of is each series convergent? \sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n^{p}}

nuais6lfp

nuais6lfp

Answered question

2021-12-02

For what values of is each series convergent?
n=1(1)n1np

Answer & Explanation

Kevin Hunt

Kevin Hunt

Beginner2021-12-03Added 20 answers

n=1(1)n1np
This is an alternating series, but for p0 we can try the Test for Divergence first to see if we can rule out convergence quickly before trying the Alternating Series Test.
If p<0 then we get
limn(1)n1n|p|=DNE
It is oscillating and doesnt

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