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October 28th, 2011, 04:05 PM   #1
JC
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inequality

Could anybody give some hint how to prove



Thanks in advance.
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October 29th, 2011, 06:39 AM   #2
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Re: inequality

Note that the inequality holds for

Next, consider the function:




You can easily show that for

This completes the proof.
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October 29th, 2011, 11:40 AM   #3
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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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October 29th, 2011, 12:50 PM   #4
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Re: inequality

Quote:
Originally Posted by JC
Thanks. Though you have some [color=#FF0000]mistakes[/color], but first of all I can't understand why the derivative may be something to judge about inequalitys correctness.
Please point out the [color=#FF0000]mistakes[/color].
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October 29th, 2011, 01:18 PM   #5
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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(x-1).
This gives f'(x) [color=#FF0000]>[/color] 0 for x > 1.
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October 29th, 2011, 02:35 PM   #6
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Quote:
Originally Posted by dibyendu
This completes the proof.
A slight exaggeration; it's important that
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October 29th, 2011, 04:32 PM   #7
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Re:

Quote:
Originally Posted by skipjack
A slight exaggeration; it's important that
Skipjack, after this comment everything is clear to me now. I solved it and understood.
Many thanks to dibyendu and skipjack.
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