Series inequality $\sum _{k=n}^{\infty } \frac{1}{k!}\leq \frac{2}{n!}$

Hint: $$\frac{1}{(n+1)!} + \frac{1}{(n+2)!} + \cdots $$ $$= \frac{1}{n!} \left( \frac{1}{(n+1)} + \frac{1}{(n+1)(n+2)} + \cdots \right) $$ $$ < \frac{1}{n!} \times \text{some geometric series}$$

Estimate it using a geometric series.