Trigonometric Series

Question

How to show that $$ \sum_{k=1}^{\infty} {\arctan{(1/k^2)}} $$ converges? I would prefer to avoid the integral test.

Can I find a more notorious convergent series that limit mine from above?

Presumably $k$ and $n$ are somehow related? – GEdgar Jan 31 '13 at 22:22 — GEdgar, Jan 31 '13 at 22:22

Emanuele Paolini · Answer 1 · 2013-12-10T16:50:45.573

11

Remember that $\lvert\arctan x\rvert \le |x|$...

edited Dec 10 '13 at 16:50

answered Jan 31 '13 at 22:10

Emanuele Paolini

1 Answers1