# Re: An inequality involving e

*From*: rob@xxxxxxxxxxxxxx (Rob Johnson)*Date*: Fri, 18 Dec 2009 15:25:47 +0000 (UTC)

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In article <92d718f6-b4ab-4e00-a244-ba6ca43555ff@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,

TCL <tlim1@xxxxxxx> wrote:

Let n be an integer >1. From the graph it is clear that

e^{-x} > (1 - x/n )^n for all x in the interval 1<= x <= n

I have a little hard time trying to prove it. Maybe some of you here

have a clever idea.

Hint: Take nth roots of both sides, then all you need to show is that

e^{-t} > 1 - t for 0 < t <= 1

Rob Johnson <rob@xxxxxxxxxxxxxx>

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