Evaluate The Following Limit (3).

Printable View

January 31st 2010, 05:46 AM
TWiX

Evaluate The Following Limit (3).

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

I can not do anything (Crying)
January 31st 2010, 06:29 AM
Archie Meade

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.

All times are GMT -8. The time now is 01:01 AM.

Copyright © 2005-2013 Math Help Forum. All rights reserved.

Copyright © 2005-2013 Math Help Forum. All rights reserved.