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Math Help - sequences of functions

  1. #1
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    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.
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  2. #2
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    Re: sequences of functions

    Quote Originally Posted by mrmaaza123 View Post
    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.
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