JEE Advance - Mathematics (2003 - No. 1)
If $$l\left( {m,n} \right) = \int\limits_0^1 {{t^m}{{\left( {1 + t} \right)}^n}dt,} $$ then the expression for $$l(m, n)$$ in terms of $$l(m+n, n-1)$$ is
$${{{2^n}} \over {m + 1}} - {n \over {m + 1}}l\left( {m + 1,n - 1} \right)$$
$${n \over {m + 1}}l\left( {m + 1,n - 1} \right)$$
$${{{2^n}} \over {m + 1}} + {n \over {m + 1}}l\left( {m + 1,n - 1} \right)$$
$${m \over {n + 1}}l\left( {m + 1,n - 1} \right)$$
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