Does the series arctan n converge?

1. Bazzinga

45
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?

2. micromass

18,536
Staff Emeritus
What is $$\lim_{n\rightarrow +\infty}{arctan(n)}$$?? Does this tell you something about convergence?

3. Bazzinga

45
pi/2, so by the test for divergence it must diverge! Ohh

4. micromass

18,536
Staff Emeritus
Correct!! A good advice: Always apply the test for divergence first!!

45
Thanks :)

Staff: Mentor

Especially since it's probably the easiest test.

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