Sum convergence test (arctan involved)

Question

I need to help with this problem:

Find out if this sum is convergent or not.

$\sum_{n=1}^\infty (arctan(n+1)-arctan(n))$

Thank's for help! :)

Before you do anything else write down a couple of partial sums. Say up to 6 and 7. Stare at them long and hard... — Jyrki Lahtonen, Jan 19 '14 at 15:47

score 3 · Answer 1 · answered Jan 19 '14 at 15:46

3

The partial sum S(k) = arctan(k+1) - arctan(1) ---> pi/2 - pi/4 = pi/4 as k --> infinity.

answered Jan 19 '14 at 15:46

DeepSea

1 Answers1