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Property:Product of r consecutive number...

Property:Product of r consecutive number is divisible by r!

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Let r consecutive positive integers be (m).
`therefore`Product=`m(m+1)(m+2) . .. (m+r-1)`
`=((m-1)!m(m+1)(m+2) . ..(m+r-1))/((m-1)!)`
`=((m+r-1)!)/((m-1)!)=(r!*(m+r-1)!)/(r!(m-1)!)" "[because.^(m+r-1)C_(r)" is natural number"]`
`=r!*^(m+r-1)C_(r)`,
which is divisible by r!.
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