# Math Help - Evaluate The Following Limit (3).

1. ## Evaluate The Following Limit (3).

Hello
$\lim_{n\to\infty} (cos(n))^n$
What the hell is this ?

I can not do anything

2. It oscillates from -1 to 0 to 1 and back again.

For natural k...

When $n=2k\pi,\ Cos(n)=1$

When $n=k\pi,\ Cos(n)=-1$
Odd powers of this is -1 and even powers is 1

When $n=k\frac{\pi}{2}, for\ k\ odd,\ Cos(n)=0$

When n = any other value, $Cos(n)$ will be between -1 and 0, or between 0 and 1, hence the infinite power will cause it to go to 0.