Answer
Determine $\rho=\lim\limits_{k \to \infty} \sqrt {a_k}$
Compare $\rho$ to 1
Work Step by Step
When $\sum a_k$ is an infinite series of nonnegative terms, in order to apply the Root Test we determine $\rho=\lim\limits_{k \to \infty} \sqrt {a_k}$.
Then we compare $\rho$ with 1 to decide if the series converges, diverges or the test is inconclusive:
- if $0\leq \rho<1$ the series converges
- if $\rho>1$ the series diverges
- if $\rho=1$ the test is inconclusive.
