1. The problem statement, all variables and given/known data For what values of p does the series [1/1^p - 1/2^p + 1/3^p - 1/4^p +... converge? 2. Relevant equations 3. The attempt at a solution I believe that this series converges for all p \in N because the sequence of a_n's is nonincreasing and converges to 0. I am not quite sure, however, to show that it converges to 0. I know that the sequence 1/n converges to 0 and I know that p is fixed, but I don't know how to massage that information into what I need. Thanks.