The greatest positive integer which divides n+1n+2n+3………n+r for all n∈N is

(n+1) (n+2) (n+3) ........ (n+r)n=1 ⇒ S(n)=1·2·3 ......... (r+1) =(r+1) !S(n) divides r !

The greatest positive integer which divides n+1n+2n+3………n+r for all n∈N is

(n+1) (n+2) (n+3) ........ (n+r)n=1 ⇒ S(n)=1·2·3 ......... (r+1) =(r+1) !S(n) divides r !

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The greatest positive integer which divides $(n + 1) (n + 2) (n + 3) \dots \dots \dots (n + r)$ for all $n \in N$ is

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n + r

r !

(r + 1) !

answer is B.

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$\begin{array}{rcl} (n + 1) (n + 2) (n + 3) . . . . . . . . (n + r) \\ n & = & 1 \Rightarrow S (n) = 1 \cdot 2 \cdot 3 . . . . . . . . . (r + 1) \\ = & (r + 1)! \end{array}$

$S (n)$ divides $r!$

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The greatest positive integer which divides n+1n+2n+3………n+r for all n∈N is

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The greatest positive integer which divides $(n + 1) (n + 2) (n + 3) \dots \dots \dots (n + r)$ for all $n \in N$ is