Q: Prove the set of {$\displaystyle S = n \epsilonN: \frac{1}{1^2} + \frac{1}{2^2} + ... + \frac{1}{n^2} <= 2 - \frac{1}{n}$} is inductive.

P.S. Are there any website or program in which I can learn more about the math coding in here? I had been spending hours inputing simply math operations. For example, I had just typed out my progress of work so far in this problem, took me about half an hour, but after I hit save, it just disappeared, did not update it, not anything. So I'm not going to type out my progress, sorry!

Thank you.