Question

How would I go about proving this. (see comments)

Answer 1

if \[a_{r} \ge 0, (r = 1,2, \cdots, n)\] then prove that \[\frac{a_{1} + a_{2} + \cdots + a_{n}}{n} \ge \sqrt[n]{a_{1}a_{2}\cdots a_{n}}\]
with equality if and only if \[a_{1} = a_{2} = \cdots = a_{n}\]

Answer 2

there are so many proofs that you get to choose the one you like best. you are going to have to use induction for sure, so google "arithmetic mean greater than geometric mean" and pick the one you like best.