InterviewSolution
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InterviewSolution
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Property:Product of r consecutive number is divisible by r! |
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Answer» Correct Answer - 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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