## Does the series arctan n converge?

I'm sure it doesn't, but how do I find out?

$$\sum^{infinity}_{n=1} arctan (n)$$

I thought about using the integral test, but it's not decreasing. Any hints?

Could I somehow use proof by induction to show that its an increasing function?
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 Mentor Blog Entries: 8 What is $$\lim_{n\rightarrow +\infty}{arctan(n)}$$?? Does this tell you something about convergence?
 pi/2, so by the test for divergence it must diverge! Ohh

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Blog Entries: 8

## Does the series arctan n converge?

Correct!! A good advice: Always apply the test for divergence first!!
 Thanks :)

Mentor
 Quote by micromass Correct!! A good advice: Always apply the test for divergence first!!
Especially since it's probably the easiest test.

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