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How to show that $e^{x} \geq \left (1 + \frac{x}{n} \right) ^{n}$ holds for each non-negative real $x$ and each integer $n \geq 1$ ? I tried series and induction but got stuck. Can you please help?

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Where did you get stuck exactly? Also, if this is homework, please consider tagging it as homework. –  Aryabhata Nov 4 '10 at 17:14
    
@Moron: Perhaps even i could have asked that question...:x)! –  anonymous Nov 4 '10 at 17:21
    
Hint : use, $\exp(y) \geq 1 + y$ for all $y$. –  ACARCHAU Nov 4 '10 at 17:27

1 Answer 1

HINT $\ $ Consider $\rm\ e^z\ \ge\ 1 + z,\ \ z\ =\ x/n $

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Thanks, this works nicely. –  student Nov 4 '10 at 18:24

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