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Inequality factorial help

  1. Oct 21, 2008 #1
    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
     
  2. jcsd
  3. Oct 21, 2008 #2

    HallsofIvy

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    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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