# Math Help - difficult induction problem

1. ## difficult induction problem

Show that if $0 \leq x < n,n \geq 1$, and $n \in \mathbb{N}$ then $0 \leq e^{-x} - \left( 1 - \frac{x}{n} \right ) ^n \leq \frac{x^2e^{-x}}{n}.$ by mathematical induction.​ 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).

2. ## Re: difficult induction problem

Hey liedora70.

One hint that may help is this:

Exponential function - Wikipedia, the free encyclopedia

Take a look a look at the limit definition and also consider the order of the function.

Big O notation - Wikipedia, the free encyclopedia