Does the series arctan n converge?

[Bazzinga]

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?

 

[micromass]

What is $$\lim_{n\rightarrow +\infty}{arctan(n)}$$?? 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]

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

Especially since it's probably the easiest test.