`(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 .

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

(1+n)C_(0)+(1+n)C_(2)+(1+n)C_(4)+ 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

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)

If n in N then hat sim(n)C_(0)+^(n+1)C_(1)+^(n+2)C_(2)+....+^(n+r)C_(i) is equal to

C_(0)-3C_(1)+5c_(3)+....+(-1)^(n)(2n+1)C_(n) is equal to