Recently learned about the monotone convergence theorem.
I have the sequence: $x_n = \frac{1}{1^2} + \frac{1}{2^2} + \cdots + \frac{1}{n^2}$
I need help proving that it is increasing and bounded, hence converges by the monotone convergence theorem.
I can see that it is monotonically increasing and it's bounded below by 1 but I'm not sure how to prove these properties. Also how do I determine and prove the upper bound for the series?
Thanks in advance.