# Does the series arctan n converge?

by Bazzinga
Tags: arctan, converge, series
 P: 41 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?
 PF Patron Sci Advisor Thanks Emeritus P: 15,673 What is $$\lim_{n\rightarrow +\infty}{arctan(n)}$$?? Does this tell you something about convergence?
 P: 41 pi/2, so by the test for divergence it must diverge! Ohh
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## Does the series arctan n converge?

Correct!! A good advice: Always apply the test for divergence first!!
 P: 41 Thanks :)
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P: 19,717
 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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