# Math Help - Finding limit

1. ## 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: $e^{-t^2/2}$)

2. ## 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.

3. ## Re: Finding limit

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