The given series is alternating, and = , and the sequence is monotone decreasing, with limit zero.
Hence, by the Leibniz test, the series converges conditionally.
However, it does not converge absolutely, as can be seen via the Limit-Comparison test, using the divergent p-series ():
=
By part (1) of the Limit-Comparison test, both series will converge or diverge, and since the -series diverges, so also does the given series if all its terms are positive.