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Theorems for Continuity

The greatest ...

Question

The greatest value of positive integer which divides $(r + 2) (r + 3) (r + 4) (r + 5) \forall r \in N$ is

4!

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2!

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5!

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3!

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Solution

The correct option is B $4!$
Let $P (r) = (r + 2) (r + 3) (r + 4) (r + 5) \forall r ϵ N$ as $r ϵ N$ means $P (r)$ is the product of four consecutive positive integer
which means $P (r)$ is the multiple of $4!$
$∴$ greatest positive integer which divides $(r + 1) (r + 2) (r + 3) (r + 4) i s 4!$

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