With the Alternating Series Test, all we need to know to determine convergence of the series is whether the limit of b[n] is zero as n goes to infinity.
So, given the series
look at the limit of the non-alternating part:
So, this series converges. Note that the other test dealing with negative numbers, the Absolute Convergence Test, would not tell us that this series converges.
If you have questions or comments, don't hestitate to contact us.