If the product of `n` positive numbers is `n^n` , then their sum is `a` positive integer b. divisible by `n` equal to `n+1//n` never less than `n^2` ``

Options

A. a positive integer
B. divisible by n
C. equal to `n+l//n`
D. never less than `n^2`

Answer

D

Explanation

Let `a_(1), a_(2)…….a_(n)` be n positive numbers such that `a_(1) a_(2)…….a_(n) = n^(2)`
Since A.M `ge` G.M we have
`(a_(1) + a_(2) + ……+ a_(n))/(n) ge (a_(1) a_(2) ……a_(n))^(1//n)`
or `(a_(1) + a_(2) + …….+ a_(n))/(n) ge n`
or `a_(1) + a_(2) + .... + a_(n) ge n^(2)`