show-proofs-by-induction-that-x-1-x-2-x-n-n-x-1-x-2-x-n-1-n-n-2-k-k-gt-1-and-x-1-x-2-x-3-x-n-gt-0-

Question Number 86672 by M±th+et£s last updated on 30/Mar/20

s h o w p r o o f s b y i n d u c t i o n, t h a t

\frac{x_{1} + x_{2} + \dots . + x_{n}}{n} ⩾ {(x_{1} x_{2} \dots . x_{n})}^{\frac{1}{n}}

\forall n = 2^{k}, k > 1 a n d (x_{1}, x_{2}, x_{3}, \dots . . x_{n}) > 0 .