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Find the value of underset(0leiltjlen)(...

Find the value of `underset(0leiltjlen)(sumsum)(-1)^(i-j+1)(.^(n)C_(i)*.^(n)C_(j))`.

Text Solution

Verified by Experts

The correct Answer is:
`n^(2)((2^(2(n-1))-.^(2(n-1))C_(n-1))/(2))`
`S=underset(lleiltjlen-1)(sumsum)(i.^(n)C_(i))(j.^(n)C_(j))`
`=n^(2)underset(lleiltjlen-1)(sumsum).^(n-1)C_(i-1).^(n-1)C_(j-1)`
`= n^(2)((2^(2(n-1))-.^(2(n-1))C_(n-1))/(2))`
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