# Math Help - a simple limit question

1. ## a simple limit question

given a(n) = (1+2/n)^n...the answer to whether the sequence converges or diverges is e^2...how do i do this?

secondly, the sequence given is (cos n)^2/(2^n)..how to find the limits?

2. Originally Posted by serenalee
given a(n) = (1+2/n)^n...the answer to whether the sequence converges or diverges is e^2...how do i do this?

secondly, the sequence given is (cos n)^2/(2^n)..how to find the limits?
1. $\lim_{n \rightarrow + \infty} \left( 1 + \frac{x}{n} \right)^n = e^x$ is a well known limit.

2. Note that $\cos n$ is bounded ....