$R=$ $\lim$

_{n →$\infty$}$\mid a_n\mid^{\frac{1}{n}}$

Where:

1. If $R$ < $1$, then the series is convergent (or absolutely convergent)

2. If $R$ > $1$, then the series is divergent

3. If $R=1$, then the series could either be divergent, or convergent

Basically if $R=1$, then the root test fails and would require a different test to determine the convergence or divergence of the series.

Note that if the root test gives $R=1$, then so will the ratio test.