Hello :D

$\displaystyle \lim_{n\to\infty} (cos(n))^n$

What the hell is this ? :(

I can not do anything (Crying)

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- Jan 31st 2010, 05:46 AMTWiXEvaluate The Following Limit (3).
Hello :D

$\displaystyle \lim_{n\to\infty} (cos(n))^n$

What the hell is this ? :(

I can not do anything (Crying) - Jan 31st 2010, 06:29 AMArchie Meade
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.