I'm a little stuck with the following inequality and was wondering if anyone could help me out.

at which point I get stuck.

I was also thinking of using the property that:

but the numerators are throwing me off.

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- September 10th 2008, 11:06 PMlllllinequality proof
I'm a little stuck with the following inequality and was wondering if anyone could help me out.

at which point I get stuck.

I was also thinking of using the property that:

but the numerators are throwing me off. - September 10th 2008, 11:49 PMMoo
Hello,

Quote:

I was also thinking of using the property that:

Quote:

but the numerators are throwing me off.

- September 11th 2008, 02:26 AMLaurent
For the numerator, use Moo's idea, and for the denominator, use indeed yours (the lower bound in the triangular inequality).

About this lower bound, it is a consequence of the usual triangle inequality: for any , , hence and by symmetry the same holds swapping and , so that .

Laurent.