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The product of n positive integers is 1, then their sum is a p

Question

The product of $n$ positive integers is $1$ , then their sum is a positive integer, that is

equal to

1

equal to

n + n^{2}

divisible by

n

never less than

n

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Liam Discussed

The product of

n

positive integers is

1

, then their sum is a positive integer, that is

14 mins ago

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14 mins ago

Text solutionVerified

Given

x_{1} . x_{2} . x_{3} ... x_{n} = 1

Since

A . M . \geq G . M .

∴ (\frac{x _{1} + x _{2} + ... + x _{n}}{n}) \geq (x_{1} . x_{2} ... x_{n})^{1/ n} = (1)^{1/ n} = 1

\Rightarrow x_{1} + x_{2} + ... + x_{n} \geq n

Hence

x_{1} + x_{2} + ... + x_{n}

can never be less than

n

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Question Text	The product of $n$ positive integers is $1$ , then their sum is a positive integer, that is
Answer Type	Text solution:1
Upvotes	150