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If (1 + x)^(n) = C(0) + C(1)x + C(2)x^(...

If `(1 + x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) +.................+ C_(n)x^(n)` then show that the sum of the products of the `C_(i)'s` taken two at a time represents by : `{:(" "sum" "sum" " c_(i)c_(j)),(0 le i lt j le n ):} ` is equal to `2^(2n-1)-(2n!)/(2.n!.n!)`

Text Solution

Verified by Experts

The correct Answer is:
`2^(2n-1)-(2n!)/(2.n!n!)`
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