Test the series for convergence or divergence using the Alternating Series test:
1. sum of (-1)^n * n/(ln n)
2. sum of [sin(n*pi/2)]/n!
The Attempt at a Solution
1. lim of n/(ln n) goes to infinity (as n->infinity), so it can't satisfy the Alternating Series test. Then if I take limit of the entire sum, I can't figure out what it comes to. I think the limit doesn't exist so the whole thing is divergent, but I'm not sure how to get it.
2. No clue on this one, it's not in the "proper format" as the examples I've seen.