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

If `(1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+..........+C_(n)x^(n)` then prove that `{:(" "sum" "sum (C_(i)+c_(j))^(2)=(n-1).^(2n)C_(n)+2^(2n)),(0 le i lt j le n ):} `

Text Solution

Verified by Experts

The correct Answer is:
`n.^(2n)C_(n)+2^(2n)-.^(2n)C_(n)=(n-1).^(2n)C_(n)+2^(2n)`
`=` R.H.S
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