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Math Help - Finding limit

  1. #1
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    Finding limit

    Hey, I've come across the following limit when trying to solve a problem in probability:

    $$ \lim_{ n \to \infty} e^{-(\sqrt{n\cdot m})it} \left(1- \frac{m}{n}(1-e^{it/\sqrt{n\cdot m}}) \right)^{n^2}$$

    Would appreciate any help!

    (I believe it should approach the characteristic function for a normal distribution:  $$e^{-t^2/2} $$)
    Last edited by MagisterMan; July 3rd 2013 at 04:04 PM.
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  2. #2
    MHF Contributor
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    Re: Finding limit

    Hey MagisterMan.

    The only advice I can give you besides any limit theorems/definitions is to transform this into a norm problem by relating the norm of |a*b| and |a+b| in terms of |a|*|b| and |a| + |b| respectively.
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  3. #3
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    Re: Finding limit

    Thanks. I actually solved the original probability problem in another way without having to solve this limit
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