Show that if $\displaystyle 0 \leq x < n,n \geq 1$, and $\displaystyle n \in \mathbb{N}$ then $\displaystyle 0 \leq e^{-x} - \left( 1 - \frac{x}{n} \right ) ^n \leq \frac{x^2e^{-x}}{n}.$ by mathematicalinduction. I suppsoe the best way is to split up the problem into two parts, one for each of the inequalitys. Doing this, I can get the base cases, but have no idea what to do with the induction step (assuming n=k and getting formula for n=k+1).