## Root Test

### Examples 4.2.14(a):

To apply the root test, we have to checkby our result on the limit of thelim sup = lim sup 1 / = 1

*n*-th root sequence. Hence, the root test, applied to the above series, is inconclusive.

However, since this series is the harmonic series, we can prove
either directly that it diverges or apply the *p*-series
test to show divergence.

Note that the root test also does not apply to the alternating harmonic series, which turns out to converge conditionally.