# Math Help - sequences of functions

1. ## 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.

2. ## Re: sequences of functions

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