Why is the following inequality true: if $x \geq 0$ then $(1-\frac{x}{n})^{n} \leq e^{-x}$ ? here $n$ is a positive integer. Is there a quick way to see this?
$(1-\frac{x}{n})^n\lt \exp(-x)$
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calculus
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0@Joe Here's a very similar StackExchange question: http://math.stackexchange.com/questions/8925/help-inequality-involving-exponential-function – 2010-11-12
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0Duplicate of http://math.stackexchange.com/questions/8925 – 2010-11-12