Find the limit of the series $6^n/n!$ as $n$ tends to infinity.

If you know about the exponential function, you can argue as follows:

The series $\displaystyle\sum_{n=0}^{\infty}\frac{6^n}{n!}$ converges to $e^6$ and so $\displaystyle\lim_{n\to\infty}\frac{6^n}{n!}=0$.