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Is this inequality true ?

  1. Mar 21, 2012 #1
    Is this inequality true ??

    [itex]0\leq \sum_{k=0}^{n} \frac{1}{(k+1)^2 (n-k+1)} \leq \frac{1}{\sqrt{n+1}} [/itex] for all natural numbers n

    Is it true ??

  2. jcsd
  3. Mar 21, 2012 #2


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    Science Advisor

    Re: Is this inequality true ??

    Can you write [tex]\frac{1}{(k+1)^2(n-k+1)}[/tex] differently? You want something on the form [tex]\frac{a}{k+1} + \frac{bk+c}{(k+1)^2} + \frac{d}{n-k+1}[/tex] .
  4. Mar 23, 2012 #3
    Re: Is this inequality true ??

    It really work thanks .
    Last edited: Mar 23, 2012
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