Understanding the First Part of an Inequality Factorial

Thread starter Unassuming
Start date Oct 21, 2008
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Factorial Inequality

Oct 21, 2008

Unassuming

Why is the first part of this inequality true?

1/(n+1)! [ (1 +1/(n+1) +1/(n+1)^{2} +...+ 1/(n+1)^{k} ]
< 1/(n!n) < 1/n

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Oct 21, 2008

HallsofIvy

Science Advisor

Homework Helper

Let a= 1/(n+1) and that sum becomes 1+ a+ a^2+ ...+ a^k, a geometric series. You can write down a simple for for it. Once you have simplified that, it should be clear.

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