- #1

- 88

- 0

**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 ??

Thanks

- Thread starter mahmoud2011
- Start date

- #1

- 88

- 0

[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 ??

Thanks

- #2

disregardthat

Science Advisor

- 1,861

- 34

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] .

- #3

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It really work thanks .

Last edited:

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