TITLE: Proving $\frac{1}{n^2}$ infinite series converges without integral test
QUESTION [14 upvotes]: Just out of curiosity, I was wondering if anybody knows any methods (other than the integral test) of proving the infinite series where the nth term is given by $\frac{1}{n^2}$ converges.

REPLY [15 votes]: With fewer words. Hopefully clear enough. Oresme's style, but converging this time,
and proving that the sum is $<2$.