## Root Test

### Examples 4.2.14(b):

To apply the root test, we have to compute the limit superior of the expressionBy our result on the limit of the(n^{2})^{1/n}= n^{2/n}= (n^{1/n})^{2}

*n*-th root sequence, the

*lim sup*of this expression is equal to 1. Hence, the root test is inconclusive.

However, the above series is a *p*-series with
*p = 2*, and therefore converges by the
*p*-series test.