I’m not sure if you mean a sequence or a series. If you want to see whether a sequence converges, try expressing the problem as a limit. If you want to see whether a series converges, write out the summation and see what it returns.
It’s of course possible that the problem might be a bit too much to expect from Wolfram|Alpha. If that’s the case, you might consider using Mathematica Online: http://www.wolframcloud.com