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## Homework Statement

I'm trying to prove that the random variable with t distribution with k degrees of freedom will have N(0,1) as k→∞ the two equations below are derived from the pdf of the t-distribution:

**2. Homework Equations which I can't get my head around**

[tex]lim_{k\to\infty}((1+\frac{x^2}{k})^k)^{-0.5} = e^{-\frac{x}{2}}[/tex]

## The Attempt at a Solution

I have proved [tex]lim_{k\to\infty}((1+\frac{x^2}{k})^{-0.5}=1 [/tex], which I admit wasn't too hard.

__The statement involving the limit of gamma function was given to us as "knowing that it can be shown" but I would appreciate if someone was willing to explain it/point me to the source where I can find it.__