Difference between revisions of "1993 USAMO Problems/Problem 5"
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== Resources == | == Resources == | ||
− | {{USAMO box|year=1993|num-b= | + | {{USAMO box|year=1993|num-b=4|a=Last Problem}} |
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=356413#p356413 Discussion on AoPS/MathLinks] | * [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=356413#p356413 Discussion on AoPS/MathLinks] |
Revision as of 15:28, 15 April 2012
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)
Solution
Resources
1993 USAMO (Problems • Resources) | ||
Preceded by Problem 4 |
Followed by [[1993 USAMO Problems/Problem {{{num-a}}}|Problem {{{num-a}}}]] | |
1 • 2 • 3 • 4 • 5 | ||
All USAMO Problems and Solutions |