Apply the ratio test to the series. Determine if the series converges, diverges, or requires a different test.

For the series, find

- If L is less than 1, the series converges.
- If L is greater than 1 (including infinity), the series diverges.
- If L is equal to 1, we need a different test.
Answer
We have
. So

(the last step is from looking at the leading terms in the numerator and denominator).
Since

the Ratio Test says this series converges.