1.

If sum_(i=0)^(2015) sum_(i=0)^(2015) C_(j)=k, then the value of (k+2)^(1//2016) is where (""^(n)C_(r) =0 AA n lt r & ""^(0)C_(0) =0}

Answer»


SOLUTION :`sum_(J=0)^(2015) sum_(i=0)^(2015) ""^(i)C_(j) = sum_(j=0)^(2015) [""^(0)C_(j) + ""^(1)C_(j) + ""^(2)C_(j) + ""^(3)C_(j) +……..+""^(2015)C_(j)]`
`2^(1) + 2^(2) + 2^(3) +……….. + 2^(2015)`
`=2(2^(2015)-1) =k`
`=2^(2016) -2 =k rArr (k+2)^(1/2016) =2`


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