Prove that the sequence space l^2 (the set of all square-summable sequences) is complete in the usual l^2 distance.
No equations.. just the definition of completeness and l^2.
The Attempt at a Solution
I have a sample proof from class to show that the space of bounded sequences l^infinity is complete in the sup-norm, but I'm having trouble adapting it. I asked some friends, and they linked me some difficult looking proofs... this is one of the early questions on my assignment so I think the modification of the proof should be straightforward. I have some intuition about cauchy sequences in l^2, but I can't seem to finish the proof.
I don't expect anyone to post a complete proof obviously, but I want to move on to the other questions soon. I would appreciate someone giving me an idea to complete this question.