## Examples 4.2.12(b):

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

But since the series1 / (1 + n^{2}) < 1 / n^{2}

*1 / n*is a

^{2}*p*-series with

*p*= 2, and therefore converges, the original series

must also converge by the comparison test.