Exercise 2.7.5

Eventually we have $1∕n^p<1∕p^n$ for $p>1$ (polynomial vs exponential) meaning we can use the comparison test to conclude ${\sum <!--\; FUNCTION\; APPLICATION\; -->}_{n=1}^{\infty }1∕n^p$ converges if $p>1$.

Now suppose $p\le 1$, since $1∕n^p\le 1∕n$ a comparsion test with the harmonic series implies $p\le 1$ diverges.