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Find the sum(r =0)^(r) ""^(n(1))C((r-i))...

Find the `sum_(r =0)^(r) ""^(n_(1))C_((r-i))""^(n_(2))C_(i)`.

Text Solution

Verified by Experts

`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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