Given n positive real numbers $a_1, a_2, . . . , a_n$ such that ${a_1}{a_2} · · ·{ an}$
= 1, prove that
$(1 + a_1)(1 + a_2) · · · (1 + a_n) ≥ 2n.$
IMO LONGLISTED PROBLEM
Re: IMO LONGLISTED PROBLEM
You meant $2^n$ right? AM-GM gives \[(1 + a_1)(1 + a_2) · · · (1 + a_n) \geq 2^n \cdot \sqrt[n] {\prod a_i}=2^n\]
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
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Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.