Find the sum `C_0+3C_1+3^2C_2++3^n C_ndot`

Important facts and formula to find Sum of Series.Find the sum C_(0)+3C_(1)+3^(2)C_(2)+......3^(n)C_(n)

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

Find the sum 1C_(0)+2C_(1)+3C_(2)+...+(n+1)C_(n), where C_(r)=^(n)C_(r)

If (1+x)^n = C_0 + C_1 x + C_2x^2 + …………+C_n x^n , find the value of C_0 - 2C_1 + 3C_2 - ……….+ (-1)^n (n+1) C_n

Find the sum 3^(n)C_(0)-8^(n)C_(1)+13^(n)C_(2)xx^(n)C_(3)+...

Find the sum of ( n + 1 ) terms of the following series 2 C_ 0 − 3 C_ 1 + 4 C_ 2 − 5 C_ 3 + ... ...

Find the sum 1xx2xx C_(1)+2xx3C_(2)+..+n(n+1)C_(n), where C_(r)=^(n)C_(r)

Find the sum : 1/2*""^(n)C_0+""^(n)C_1+2*""^(n)C_2+2^2*""^nC_3+...+2^(n-1)*""^(n)C_n .

Find the sum 2C_(0)(23)/(2)quad C_(1)+(2^(3))/(3)C_(2)+(2^(4))/(4)C_(3)+...+(2^(11))/(11)C_(10)