Is this inequality true ?

1. Mar 21, 2012

mahmoud2011

Is this inequality true ??

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

Is it true ??

Thanks

2. Mar 21, 2012

disregardthat

Re: Is this inequality true ??

Can you write $$\frac{1}{(k+1)^2(n-k+1)}$$ differently? You want something on the form $$\frac{a}{k+1} + \frac{bk+c}{(k+1)^2} + \frac{d}{n-k+1}$$ .

3. Mar 23, 2012

mahmoud2011

Re: Is this inequality true ??

It really work thanks .

Last edited: Mar 23, 2012