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Question

The product of n positive numbers is nn, then their sum is:

A
A positive integer
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B
Divisible by n
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C
Equal to n+1n
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D
Never less than n2
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Solution

The correct option is D Never less than n2
We know that A.M.G.M.

A.M. of n positive numbers is 1+2+3+...+nn

G.M. of n positive numbers is n123...n

Given that product of n positive numbers is nn

Therefore, G.M. is nnn=n

Hence, 1+2+3+...+nnn

1+2+3+...+nn2

Therefore, the sum of n positive numbers is never less than n2

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