Hello
$\displaystyle \lim_{n\to\infty} (cos(n))^n$
What the hell is this ?
I can not do anything
It oscillates from -1 to 0 to 1 and back again.
For natural k...
When $\displaystyle n=2k\pi,\ Cos(n)=1$
When $\displaystyle n=k\pi,\ Cos(n)=-1$
Odd powers of this is -1 and even powers is 1
When $\displaystyle n=k\frac{\pi}{2}, for\ k\ odd,\ Cos(n)=0$
When n = any other value, $\displaystyle Cos(n)$ will be between -1 and 0, or between 0 and 1, hence the infinite power will cause it to go to 0.