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Does the series arctan n converge?

by Bazzinga
Tags: arctan, converge, series
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Bazzinga
#1
Mar1-11, 02:28 PM
P: 42
I'm sure it doesn't, but how do I find out?

[tex]\sum^{infinity}_{n=1} arctan (n)[/tex]

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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micromass
#2
Mar1-11, 03:11 PM
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What is [tex]\lim_{n\rightarrow +\infty}{arctan(n)}[/tex]?? Does this tell you something about convergence?
Bazzinga
#3
Mar1-11, 03:28 PM
P: 42
pi/2, so by the test for divergence it must diverge! Ohh

micromass
#4
Mar1-11, 03:33 PM
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Does the series arctan n converge?

Correct!! A good advice: Always apply the test for divergence first!!
Bazzinga
#5
Mar1-11, 03:34 PM
P: 42
Thanks :)
Mark44
#6
Mar1-11, 08:41 PM
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Quote Quote by micromass View Post
Correct!! A good advice: Always apply the test for divergence first!!
Especially since it's probably the easiest test.


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