Does the series arctan n converge?

Bazzinga

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?

micromass

What is [tex]\lim_{n\rightarrow +\infty}{arctan(n)}[/tex]?? Does this tell you something about convergence?

Bazzinga

pi/2, so by the test for divergence it must diverge! Ohh

micromass

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

Bazzinga

Thanks :)

Mark44

Especially since it's probably the easiest test.