1993 USAMO Problems/Problem 5
Let be a sequence of positive real numbers satisfying
for
. (Such a sequence is said to be log concave.) Show that for
each
,
![$\frac{a_0+\cdots+a_n}{n+1}\cdot\frac{a_1+\cdots+a_{n-1}}{n-1}\ge\frac{a_0+\cdots+a_{n-1}}{n}\cdot\frac{a_1+\cdots+a_{n}}{n}$](http://latex.artofproblemsolving.com/d/a/2/da21136d8f04ee35b3510f5fb8653b483dc8131b.png)
Let be a sequence of positive real numbers satisfying
for
. (Such a sequence is said to be log concave.) Show that for
each
,
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