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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)` ,
find the values of the following
`underset(0leilt j le n)(sumsum)jC_(i)`

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Verified by Experts

`underset(0leilt j le n)(sumsum)C_(i)= ((sum_(i=0)^(n) underset(j=0)overset(n)sum) C_(i)-underset(i= j)(sumsum)C_(i))/(2)`
` = ((n+1)sum_(i=0)^(n) C_(i) sum_(i=0)^(n)C_(i))/(2) = n.2^(n-1)`
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