Sequence And Series Question 168
Question: The product of $ n $ positive numbers is unity. Their sum is
[MP PET 2000]
Options:
A) A positive integer
B) Equal to $ n+\frac{1}{n} $
C) Divisible by $ n $
D) Never less than
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Answer:
Correct Answer: D
Solution:
Given $ x_1.x_2.x_3……….x_{n}=1 $ $ \because $ $ A\text{.M}\text{.},\ge G\text{.M}\text{.} $ \ $ ( \frac{x_1+x_2+x_3+……+x_{n}}{n} ),\ge ,{{(x_1.x_2.x_3…….x_{n})}^{\frac{1}{n}}} $ $ ={{(1)}^{\frac{1}{n}}}=1 $ \ $ x_1+x_2+x_3+……..+x_{n}\ge n $ \ $ x_1+x_2+x_3+…….+x_{n} $ can never be less than n.
BETA
