trigonometric series

[gbuzzle]

i've got this series

the SUM of (arctan n) from n=1 to infinity. does it converge or diverge?


well since its trigonometric and obviously oscillates, i think it diverges...but i feel i need to say more than just an intuitive reason. should i just draw a graph or something?



thanks a bunch guys

 

[soroban]

Hello, gbuzzle!

I've got this series

. . ∞
. . ∑ arctan n . . Does it converge or diverge?
. ⁿ⁼¹

well since its trigonometric and obviously oscillates . . . no, it doesn't

It diverges because its n^th term does not go to 0 . . . it goes to π/2