Monday, March 26, 2018

induction - Inequality in Algebra: 1leqx1x2cdotsxn implies that 2nleq(1+x1)(1+x2)cdots(1+xn).

How do I prove that if x1,,xn are positive real numbers, then

1x1x2xn implies that 2n(1+x1)(1+x2)(1+xn).



I attempted a proof by induction but am not able to nail the inductive step. Any help would be appreciated!

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