`(n+2)C_0(2^(n+1))-(n+1)C_1(2^(n))+(n)C_2(2^(n-1))-....` is equal to

If the value of (n + 2) . ""^(n)C_(0) *2^(n+1) - (n+1) * ""^(n)C_(1)*2^(n) + n* ""^(n)C_(2) * 2^(n-1) -... is equal to k(n +1) , the value of k is .

If the value of (n + 2) . ""^(n)C_(0) *2^(n+1) - (n+1) * ""^(n)C_(1)*2^(n) + n* ""^(n)C_(2) * 2^(n-1) -... is equal to k(n +1) , the value of k is .

The value of (n+2).^(n)C_(0).2^(n+1)-(n+1).^(n)C_(1).2^(n)+(n).^(n)C_(2).2^(n-1)-….." to " (n+1) terms is equal to

The value of hat r(2n+1)C_(0)^(2)+^(2n+1)C_(1)^(2)+^(2n+1)C_(2)^(2)+....+^(2n+1)C_(n)^(2) is equal to

If n = 5, then (""^(n)C_(0))^(2)+(""^(n)C_(1))^(2)+(""^(n)C_(2))^(2)+......+(""^(n)C_(5))^(2) is equal to

The sum of the series 1+(1)/(2)""^(n)C_(1)+(1)/(3)""^(n)C_(2)+…+(1)/(n+1)""^(n)C_(n) is equal to-

C_(0)^(n)C_(n)^(n+1)+C_(1)^(n)C_(n-1)^(n)+C_(2)^(n)*C_(n-2)^(n-1)+.........+C_(n)^(n)*C_(0)^(1)=2^(n-1)(n+2)