Difference between revisions of "1989 APMO Problems/Problem 1"
(Created page with "==Problem== Let <math>x_1</math>, <math>x_2</math>, <math>\cdots</math>, <math>x_n</math> be positive real numbers, and let <cmath> S = x_1 + x_2 + \cdots + x_n. </cmath> Pro...") |
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Latest revision as of 21:54, 11 July 2021
Problem
Let 
, 
, 
, 
be positive real numbers, and let
![\[S = x_1 + x_2 + \cdots + x_n.\]](http://latex.artofproblemsolving.com/0/1/1/0111387dc55dafd7e8177f5ae5e1ae74b087dcb5.png)
Prove that
![\[(1 + x_1)(1 + x_2) \cdots (1 + x_n) \leq 1 + S + \frac{S^2}{2!} + \frac{S^3}{3!} + \cdots + \frac{S^n}{n!}\]](http://latex.artofproblemsolving.com/7/6/1/761b88aea2702bf9ff4bfdf260f8bd25df1c85c1.png)
