Question

Prove that for any xj ≥ 0 for all 1 ≤ j ≤ n we have...

Prove that for any

xj ≥ 0 for all 1 ≤ j ≤ n

we have

(x1x2 . . . xn)1/n ≤ (x1 + x2 + · · · + xn)/n.

In other words, the geometric mean of n non-negative numbers is smaller or equal to their arithmetic mean

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