How do I show that as $\displaystyle n\to\infty$ of $\displaystyle (1-\frac{x}{\theta n})^n$ = $\displaystyle e^{-\frac{x}{\theta}}$??
Hello,
Note that :
$\displaystyle \left(1-\frac{x}{n \theta}\right)^n=\left(\left(1-\frac{x}{n \theta}\right)^{-n\theta/x}\right)^{-x/\theta}$
Substitute $\displaystyle \frac 1t=-\frac{x}{n \theta}$ and you will get :
$\displaystyle \lim_{t \to \infty} \left(\left(1+\frac 1t\right)^t\right)^{-x/\theta}$
and this is a known formula