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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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  • $\begingroup$ Hint : use, $\exp(y) \geq 1 + y$ for all $y$. $\endgroup$ – Arin Chaudhuri Nov 4 '10 at 17:27
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HINT $\ $ Consider $\rm\ e^z\ \ge\ 1 + z,\ \ z\ =\ x/n $

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  • $\begingroup$ Thanks, this works nicely. $\endgroup$ – student Nov 4 '10 at 18:24

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