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TT2008 Junior A-Level - P5

Source:

September 4, 2010
inequalitiesinequalities proposed

Problem Statement

Let a1,a2,⋯ ,ana_1,a_2,\cdots,a_n be a sequence of positive numbers, so that a1+a2+⋯+an≤12a_1 + a_2 +\cdots + a_n \leq \frac 12. Prove that (1+a1)(1+a2)⋯(1+an)<2.(1 + a_1)(1 + a_2) \cdots (1 + a_n) < 2.
[hide="Remark"]Remark. I think this problem was posted before, but I can't find the link now.
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