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BITSAT 2014
Exam
BITSAT
Year
2014
Subject
Mathematics
Chapter
Sequences and Series

BITSAT 2014 · Mathematics · Sequences and Series

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

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

Options

  1. Aa positive integer
  2. Bdivisible by nn
  3. Cequal to n+1nn+\frac{1}{n}
  4. Dnever less than nn

Correct answer

D. never less than nn

Step-by-step solution

Since, product of nn positive number is unity. ⇒x1x2x3……xn=1\Rightarrow x_{1} x_{2} x_{3} \ldots \ldots x_{n}=1 Using A.M. \geq GM ⇒x1+x2+…..+xnn≥(x1x2……xn)1n⇒x1+xn+……+xn≥n(1)1n[ From eq n(i)]\begin{array}{l} \Rightarrow\frac{x_{1}+x_{2}+\ldots . .+x_{n}}{n} \geq\left(x_{1} x_{2} \ldots \ldots x_{n}\right)^{\frac{1}{n}} \\ \Rightarrow x_{1}+x_{n}+\ldots \ldots+x_{n} \geq n(1)^{\frac{1}{n}}\left[\text{ From eq }^{\mathrm{n}}(\mathrm{i})\right] \end{array}
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