# Does the series arctan n converge?

1. Mar 1, 2011

### 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?

2. Mar 1, 2011

### micromass

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

3. Mar 1, 2011

### Bazzinga

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

4. Mar 1, 2011

### micromass

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

5. Mar 1, 2011

Thanks :)

6. Mar 1, 2011

### Staff: Mentor

Especially since it's probably the easiest test.