Mathematics - Sequence & Series Question with Solution | TestHub

For $1,a_1,a_1^2$ : A.M. $\ge$ G.M. gives $\frac{1+a_1+a_1^2}{3}\ge {\left(a_1^3\right)}^{1/3}=a_1$, so $1+a_1+a_1^2\ge 3a_1$. Similarly for each $a_i$. Multiplying: product $\ge 3^n{a}_1{a}_2\cdots a_n=3^n$. Equality holds at all $a_i=1$.