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The greatest positive integerwhich divides (n+1)(n+2)(n+3) upto (n+r) forall n belongs to N is a)r! b)(r+1)! I think option b) is correct .If not .Please explain in detail.

The greatest positive integerwhich divides (n+1)(n+2)(n+3) upto (n+r) forall n belongs to N is                         a)r!   b)(r+1)!   I  think option b) is correct .If not .Please explain in detail.

Grade:12

1 Answers

Arun
25763 Points
3 years ago
 
Dear student
 
P(n) = (n+1)(n+2).........(n+r)
 
Now find p(1)
P(1) = r! (r+1)
 
Similarly
P(k) will be divisible by r!
P(k+1) is also divisible by r!
 
Hence p(n) qill also be divisible by r!.

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