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Find the sum (sumsum)(0leiltjlen) ""^(n)...

Find the sum `(sumsum)_(0leiltjlen) ""^(n)C_(i).""^(n)C_(j)`.

Text Solution

Verified by Experts

`underset(0leiltjlen)(sumsum).^(n)C_(i) = ((underset(i=0)overset(n)sumunderset(j=0)overset(n)sum.^(n)C_(i))-underset(i=0)overset(n)sum.^(n)C_(i))/(2)`
`= ((underset(i=0)overset(n)sum(n+1)^(n)C_(i))-underset(i=0)overset(n)sum.^(n)C_(i))/(2)`
` = ((n+1)2^(n)-2^(n))/(2)`
`= n xx 2^(n-1)`
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