# sequences of functions

• Mar 11th 2013, 12:00 AM
mrmaaza123
sequences of functions
Show that lim((cos pix)2n) exists for all x in R ?

I figured that the limit will be 1 when x belongs to Z and 0 otherwise.
But how can i show that the limit actually exists?

Help will be appreciated.
• Mar 11th 2013, 05:24 AM
Plato
Re: sequences of functions
Quote:

Originally Posted by mrmaaza123
Show that lim((cos pix)2n) exists for all x in R ?
I figured that the limit will be 1 when x belongs to Z and 0 otherwise.
But how can i show that the limit actually exists?

I don't really know what you mean by showing.

We all know that $(x)^{2n}\to 1,~|x|=1~\&~(x)^{2n}\to 0,~|x|<1.$