Find the sum of the following
`2^(2).C_(0)+3^(2).C_(1)+4^(2).C_(2)+…..+(n+2)^(2)C_(n)`

Find the sum of the following C_(0).C_(3)+C_(1).C_(4)+C_(2).C_(5)+…+C_(n-3).C_(n).

Find the sum of the following 3C_(0)+6C_(1)+12C_(2)+…..+3.2^(n).C_(n)

Find the sum of the following C_1 + 2^2 C_2 + 3^2 C_3 + ... + n^2C_n

Find the sum of the following 1.2 C_(2) + 2.3 C_(3) + ... + (n-1)nCn

Find the sum of the series .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1).^(n)C_(n)x^(n) and hence show that , .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1)^(n)C_(n)=(n+2)2^(n-1)

If n is odd, then sum of the series C_(0)^(2)-C_(1)^(2)+C_(2)^(2)-C_(2)^(3)+…..+(-1)^(n)C_(n)^(2) is

Find the sum 1.^(n)C_(0) + 3 .^(n)C_(1) + 5.^(n)C_(2) + "….." + (2n+1).^(n)C_(n) .

Find the sum .^(n)C_(0) + 2 xx .^(n)C_(1) + xx .^(n)C_(2) + "….." + (n+1) xx .^(n)C_(n) .

Prove that following C_(0)+2.C_(1)+4.C_(2)+8.C_(3)+…+2^(n).C_(n)=3^(n)