Prove that the product of r consecutive positive integers is divisible by r'
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This type of theorem can be proved by considering a sequence of numbers
The product of r consecutive integer can be represented as
(n+r)(n+r-1).....(n+1) = (n+r)!/ n!
where n is the number less than the smallest of the consecutive integers. Now, if it is true that prime in (n+r)! appear just as frequently or more as in
n!r! ,then now for same integer k that (n+r)! = k.n!r!
so, (n+r)!/n! = k.n!r!/n!} = k.r!
and is therefore divisible by r!.
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