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Prove the arithmetic-geometric mean inequality.

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Prove the arithmetic-geometric mean inequality by using an elementary method (no use of calculus, derivative or limit), that is,

(X1...Xn)^1/n <= (X1+...+Xn)/n

for non-negative real numbers X1, X2, ..., Xn.

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The expert proves an arithmetic geometric mean inequality.

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Please find attached a simple inductive proof in .docx and .pdf format.

Consider the inequality

(1) (X1...Xn)^1/n <= (X1+...+Xn)/n for ...

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