Determine if the following alternating series converges. Is it absolutely convergent?
Using the alternating series test, we need:
a) > 0 for all k > 1
b) for all k > 1
c) Limit is obviously 0 as
Thus the series converges.
Now we consider
Using ratio test:
Therefore converges. So this series should be absolutely convergent. However the answer is actually 'conditionally convergent'.
Where have I gone wrong? Thanks.