Question

If the product of n positive numbers is $n^n$, then their sum is

• A. never less than
• B. always greater than + 1
• C. greater than n + 2
• D. equal to n +

Answer 1

The correct option is A

never less than

Let $a_1$, $a_2$, ---------$a_n$ be n positive integers such that their product $a_1$, $a_2$,-----------$a_n$ = $n^n$. We know that

AM $\ge$ GM $\ge$ HM

Taking AM $\ge$ GM

$\frac{a_1+a_2+---------+a_n}{n}$ $\ge$ ${(a_1,a_2,---------a_n)}^{\frac{1}{n}}$

$\Rightarrow$ $a_1$ + $a_2$+ ---------+$a_n$ $\ge$ $n^2$

So, A is right option