Limit of Series - Help!

Could anyone help me to find out how to prove this:

lim[n-->inf] ( 1/n² + 1/(n+1)² + 1/(n+2)² + ... + 1/(2n)² ) = 0 ?

I tried to make it a sum like sum(i=0 to n)(1/(n+i)²) but anyway could't go much further.
I Thank you guys in advance ;)

We know that each of the terms is less than or equal to 1/n². Since there are n+1 terms, for each n the sum of the terms is less than or equal to (n+1)/n² = 1/n² + 1/n, which goes to zero as n goes to infinity.

I have a feeling that you may soon be show a proof that the harmonic series, the sum of the terms 1/n, goes to infinity. There is a very short and clever proof that uses the idea of a series comparison, like the proof to this problem. If you are not shown the proof soon, let me know. It is something that everyone should get a chance to see.

Actually it is not a series
general term an is the sum of the reciprocal of the squares from n to 2n

an = 1/n² + 1/(n+1)² + 1/(n+2)² + ... + 1/(2n)² <

< 1/n² + 1/n² + 1/n² + ... + 1/n² = n/n² = 1/n

an < 1/n (for n > 3)

as lim 1/n = 0 and an > 0 for any n
then
lim an = 0

I hope it helps