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## Homework Statement

[tex]\sum_{n=2}^{\infty} \ln \left(1+\frac{(-1)^n}{n^p}\right)[/tex]

p is a real parameter, determine when the series converges absolutely/non-absolutely

## The Attempt at a Solution

I tried to do the limit [tex]\lim_{n\rightarrow \infty} \frac{\ln \left(1+\frac{(-1)^n}{n^p}\right)}{\frac{(-1)^n}{n^p}}[/tex], which is equal to one and this suggests that the series coverges if p is positive (limit comparison test). But then I'm not sure how to determine the absolute/non-absolute convergence. Could you help me please? Thanks very much in advance!

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