prove that 1+1/4+.........+1/n^2<2-1/n
true for k=1?
1/1^2 < 2 - 1/1 ?
no. well, maybe
1 + 1/2^2 < 2 - 1/2 ?
5/4 < 3/2 ?
yes. So, we'll do induction for k>2
assume
∑ 1/k^2 < 2 - 1/k
now show that
∑ 1/k^2 + 1/(k+1)^2 = 2 - 1/k + 1/(k+1)^2 < 2 - 1/(k+1)^2
see what you can do with that.
I bet google can help if you still get stuck.