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Find the sum sum(i=0)^r^(n1)C(r-i)^(n2)C...

Find the sum `sum_(i=0)^r^(n_1)C_(r-i)^(n_2)C_i` .

Text Solution

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`S = underset(i=0)overset(r )sum (.^(n_(1))C_(r-i))(.^(n_(2))C_(i))`
`= "Coefficient of" x^(r ) "in"(1+x)^(n)(1+x)^(n_(2))`
`.^(n_(1)+n_(2))C_(r)`
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