Difference between revisions of "1993 USAMO Problems/Problem 5"

Revision as of 13:29, 4 July 2013

Problem 5

Let $a_0, a_1, a_2,\cdots$ be a sequence of positive real numbers satisfying $a_{i-1}a_{i+1}\le a^2_i$ for $i = 1, 2, 3,\cdots$ . (Such a sequence is said to be log concave.) Show that for each $n > 1$ ,

$\frac{a_0+\cdots+a_n}{n+1}\cdot\frac{a_1+\cdots+a_{n-1}}{n-1}\ge\frac{a_0+\cdots+a_{n-1}}{n}\cdot\frac{a_1+\cdots+a_{n}}{n}$ .

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

@@ Line 16: / Line 16: @@
 [[Category:Olympiad Algebra Problems]]
 [[Category:Olympiad Inequality Problems]]
+{{MAA Notice}}

1993 USAMO (Problems • Resources)
Preceded by Problem 4	Followed by Last Problem
1 • 2 • 3 • 4 • 5
All USAMO Problems and Solutions

Page

Toolbox

Search

Difference between revisions of "1993 USAMO Problems/Problem 5"

Revision as of 13:29, 4 July 2013

Problem 5

Solution

See Also