inequality Could anybody give some hint how to prove Thanks in advance. 
Re: inequality Note that the inequality holds for Next, consider the function: You can easily show that for This completes the proof. 
Re: inequality Thanks. Though you have some mistakes, but first of all I can't understand why the derivative may be something to judge about inequality's correctness. 
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Re: inequality I think you thought f(x) = 1 / ((x+1) sqrt(x))  2tan^(1) sqrt(x) [color=#FF0000]+[/color] 2tan^(1) sqrt(x1). This gives f'(x) [color=#FF0000]>[/color] 0 for x > 1. 
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Many thanks to dibyendu and skipjack. 
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