Question

the series involving 1/n^p is convergent if p____​

Answer 1

Answer:

The series involving 1/n^p is convergent only if p>1

Note that even when p=1 , the series will become divergent hence p>1 (must be greater than 1)

In a naive way the reason is the divergence of the integral 1/x dx from 1 to infinity.

Certainly, some conditions over n are also needed to completely understand the convergence of a given series.