Prove by induction that for $n\geq1$, $(a_1+a_2+...+a_n)/n \geq (a_1a_2...*a_n)^{1/n}$

Asked Sep 10 '17 at 15:40

Active Sep 10 '17 at 15:40

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Prove by induction that for $n\geq1$, $(a_1+a_2+...+a_n)/n \geq (a_1*a_2*...*a_n)^{1/n}.$ I proved the base case, not sure how to do the inductive step. The values of the sequence are greater than or equal to zero.

asked Sep 10 '17 at 15:40

Jack Pan

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It's the AM/GM inequality. – Angina Seng Sep 10 '17 at 15:42
1

This is the AM-GM (Arithmetic Mean -- Geometric Mean) inequality. There are plenty of sites in internet with the proof. – ajotatxe Sep 10 '17 at 15:42

Prove by induction that for $n\geq1$, $(a_1+a_2+...+a_n)/n \geq (a_1*a_2*...*a_n)^{1/n}$

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Prove by induction that for $n\geq1$, $(a_1+a_2+...+a_n)/n \geq (a_1a_2...*a_n)^{1/n}$