CGMO 2012 (China Girls Math Olympiad 2012) Problem 1


Let  a_{1}, a_{2},\ldots, a_{n} be non-negative real numbers. Prove that                                                                          \LARGE \frac{1}{1+a_{1}}+\frac{ a_{1}}{(1+a_{1})(1+a_{2})}+\frac{ a_{1}a_{2}}{(1+a_{1})(1+a_{2})(1+a_{3})}\cdots+\frac{ a_{1}a_{2}\cdots a_{n-1}}{(1+a_{1})(1+a_{2})\cdots (1+a_{n})}\le 1.

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About shivang1729

I am a young student who loves math . I like number theory and inequalities part the most , and preparing for Math Olympiads :)

Posted on Saturday,August 18, 2012, in inequalities, Problems and tagged , , , , . Bookmark the permalink. Leave a comment.

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