Question

The product of n positive numbers is unity, then their sum is

• A. a positive integer
• B. divisible by n
• C. equal to $n+\frac{1}{n}$
• D. never less than n

Answer 1

Answer: (D)

never less than n

Answer 2

Since, product of n positive numbers is unity.
\hspace30mm x_1. x_2. x_3 ...x_n = 1 \hspace30mm ...(i)
$Using\, AM \ge GM, \frac{x_1+ x_2+ ...+x_n}{n} \ge (x_1. x_2....x_n)^{1/n}$
\hspace30mm x_1+ x_2+ ... +x_n \ge n\, (1)^{1/n}\hspace5mm [from E (i)]
Hence, sum of n positive numbers is never less than n.