What is the Limit of the Sequence {arctan(2n)} and Does it Converge to pi/2?

[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?

 

[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.

 

[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.