Questions
The product of r consecutive positive integers is divisible by
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a
r!
b
(r – 1)!
c
(r + 1)!
d
None of these
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Correct option is A
Let r consecutive positive integers bem, m + 1, m + 2, … (m + r – 1), where m ∈ N∴ 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)!=r!⋅m+r−1Crwhich is divisible by r! (∵ m + r – 1Cr is a natural number)Similar Questions
is equal to
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