Chapter 5.1, Problem 63E

& 63.Leta₁,a₂,...,a_nbe positive real numbers. The arithmetic mean of these numbers is defined by

**emsp;  $\begin{array}{l}A=\left(a_1+a_2+\mathrm{...}+a_n\right)/n\\ G=\end{array}$

and the geometric mean of these numbers is defined by

   ${\left(a_1,a_2\mathrm{...}{a}_n\right)}^{1/n}$

Use mathematical induction to prove thatA >G.