Evaluate The Following Limit (3).

**TWiX** · January 31st 2010, 05:46 AM

Hello

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

I can not do anything

**Archie Meade** · January 31st 2010, 06:29 AM

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.

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