Finding $\lim_{n \to \infty} n (e^{1/n} - 1)$ 
Find $\lim_{n \to \infty} n (e^{1/n} - 1)$.

Could anyone give me a hint please?

MVT:
$\displaystyle {\int_{0}^{1/n}}e^x dx =e^{1/n} -1 =(1/n) e^t,$  $t \in [0,1/n].$
$1\le n(e^{1/n}-1) =e^t \le e^{1/n}.$
