Determine if the following series converges or diverges and justify your decision.

This series converges. First, we make the comparison,

Then, for this series we use the ratio test, denoting the terms by we have,

Hence, the series converges; therefore,

converges as well.

You can also use the root test

the limit of the nth root does not exist, the terms keep oscillating so the root test fails

I think he might mean on the series we’re comparing to the original one (with a plus one instead of plus (-1)^n)