# Convergence of arctan(2n)

1. Nov 13, 2007

### Schecter5150

For the sequence {arctan2n}, it is bounded by pi/2, so does that mean it converges to pi/2, because the limit of f(x) = L, and therefore the limit of the sequence is pi/2?

Last edited: Nov 13, 2007
2. Nov 13, 2007

### EnumaElish

Here is an example of a sequence: 1, 1/2, 1/4, 1/8, ...

It is bounded by 1, but does not converge to 1.

Therefore, you need other conditions.

3. Nov 14, 2007

### NeoInTheMatrix

Your other condition is that its monotonic increasing in n. And there's a theorem that says it converges to the sup of {arctan(2n): n>0}, which is pi/2.