dobry_den
- 113
- 0
Homework Statement
\sum_{n=2}^{\infty} \ln \left(1+\frac{(-1)^n}{n^p}\right)
p is a real parameter, determine when the series converges absolutely/non-absolutely
The Attempt at a Solution
I tried to do the limit \lim_{n\rightarrow \infty} \frac{\ln \left(1+\frac{(-1)^n}{n^p}\right)}{\frac{(-1)^n}{n^p}}, 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!
Last edited: