Find all possible values of the positive constant k such that the series
$$\sum_{n=1}^{\infty}\ln\left(1+\frac{1}{n^k}\right)$$
is convergent.
Definitely not root test. Tried ratio test, $L = 1$ which is not conclusive.
Tried integral test but the integral looks too hideous to evaluate.
Any other suggestions?
How do I come up with the series to compare with? Keep practising?
For this question, in my mind, I would compare it with another logarithm and not even think about riemann series.