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Math Help - Convergence of continuous function

  1. #1
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    Convergence of continuous function

    My professor hinted that this problem would be on the final, so any help would be greatly appreciated.

    Find:
    limit as n goes to infinity of (limit as k goes to infinity of cos((n!*pi*x)^2k))

    I know since it's continuous, I should be able to move the limits inward, but I don't know if that's the right way to go about this problem. I'll take any suggestions please.
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  2. #2
    MHF Contributor chisigma's Avatar
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    First we 'fix' n and define...

    (1)

    ... and leaving undefined for all other values of x. Now what is the limit when n tends to infinity of ?...

    Kind regards

    \chi \sigma
    Last edited by chisigma; May 3rd 2011 at 06:43 AM. Reason: trivial error: x instead of n... sorry!...
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