Limit $\lim_{n \to \infty} n (1 - \mathrm{e}^{t/n})$

Can someone help how to compute (step-by-step) the following limit? When I use the online calculator, the answer is -t. However, I do not know how to get that answer.

$$\lim_{n \to \infty} n (1 - \mathrm{e}^{t/n})$$

Thanks

• All the hints are very useful. I finally understood the method to do by replacing the new variable, such as y = 1/n in the equation. Then, I did one time L^Hopital's Rule. Finally I got -t. – user105692 Dec 4 '13 at 3:17

$$e^{t/n} = 1+\frac{t}{n}+\dots \,.$$
HINT: Recall $$\lim_{x \to 0} \dfrac{e^{ax}-1}x =a$$