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If $l (m, n) = \int_{0}^{1} t^{m} (1 + t)^{n} d t$ then the expression for $l (m, n)$ in terms of $l (m + 1, n - 1)$ is

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2nm+1−nm+1l(m+1,n−1)

nm+1l(m+1,n−1)

2nm+1+nm+1l(m+1,n−1)

mn+1l(m+1,n−1)

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Correct option is A

I(m,n)=1m+1tm+1(1+t)n01−nm+1I(m+1,n−1)⇒I(m,n)=2nm+1−nm+1I(m+1,n−1)

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If l(m,n)=∫01 tm(1+t)ndt then the expression for l(m,n) in terms of l(m+1,n−1) is

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If $l (m, n) = \int_{0}^{1} t^{m} (1 + t)^{n} d t$ then the expression for $l (m, n)$ in terms of $l (m + 1, n - 1)$ is