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Property:Product of r consecutive number...

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

Text Solution

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The correct Answer is:
True
Let r consecutive integers be x + 1, x + 2,.., x + r.
`therefore (x +1 )(x + 2) .. (x + r) = ((x + r)(x + r - 1)..(x + 1)x!)/(x!)`
`= ((x + r)!)/((x)!)*(r!)/(r!) = ""^(x + r)C_(r)*(r)!`
Thus, `(x + 1)(x + 2)…(x + r) = ""^(x + r)C_(r)*(r)!`, which is clearly divisible by `(r)!`. Hence, it is a true statement.
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