## Theorem 4.2.11: p Series

### Examples 4.2.12(c):

We will use the limit comparison test, together with the
*p*-series test. First, note that

Hence, by the limit comparison test, the two series

and

have the same convergence behavior. But the second series is a1 /

*p*-series with

*p = 1/2*, so it diverges by the

*p*-series test. Hence, the original series also diverges.