Prove that the series whose terms are 1/n^2 converges by showing that the partial sums form a Cauchy sequence.

I've tried to start this as follows: Assuming that m>n, we have

|a_n-a_m|=1/m^2+1/(m+1)^2+...+1/(n+1)^2 <= (m-n)/(n+1)^2.

So to show it's Cauchy, I need to find N such that m,n>N implies |a_n-a_m|<epsilon for any epsilon. But how can I find this? Don't I have to somehow eliminate m from the expression? I don't know how to do this. Help!