1.

The value of the expansion (sumsum)_(0 le i lt j le n) (-1)^(i+j-1)"^(n)C_(i)*^(n)C_(j)=

Answer»

`"^(2n-1)C_(N)`
`"^(2n)C_(n)`
`"^(2n+1)C_(n)`
None of these

Solution :`(a)` LET the required value be `S`
`sum_(j=0)^(n)sum_(i=0)^(n)(-1)^(i+j-1)'^(n)C_(i)*^(n)C_(j)=sum_(i=0)^(n)(-1)^(2i-1)('^(n)C_(i))^(2)+2S`
`:.0=-sum_(i=0)^(n)('^(n)C_(i))^(2)+2S`
`:.2S=^(2n)C_(n)`
`:.S=^(2n-1)C_(n-1)=^(2n-1)C_(n)`


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