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Math Help - difficult induction problem

  1. #1
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    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).
    Last edited by liedora70; February 9th 2014 at 07:08 PM.
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  2. #2
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    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
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