`2.C_0+(2^2.C_1)/2+(2^3.C_2)/3+(2^4.C_3)/4+............+(2^(n+1).C_n)/(n+1)=(3^(n+1)-1)/(n+1)`

If (1+x)^n=C_0+C_1x+C_2x^2+C_3x^3+...+C_nx^n then prove that 2.C_0+2^2C_1/2+2^3C_2/3+2^4C_3/4+...+2^(n+1)C_n/(n+1)=(3^(n+1)-1)/(n+1)

2C_0 + 2^2 (C_1)/(2) + 2^3 (C_2)/(3) + ………. + 2^(n+1) (C_n)/(n+1) = (3^(n+1) - 1)/(n+1)

C_(0)-(C_(1))/(2)+(C_(2))/(3)-............(-1)^(n)(C_(n))/(n+1)=(1)/(n+1)

C0-(C1)/(2)+(C2)/(3)-............+(-1)^(n)(Cn)/(n+1)=(1)/(n+1)

4C_(0)+(4^(2))/(2)*c_(1)+(4^(3))/(3)c_(2)+............+(4^(n+1))/(n+1)C_(n)=(5^(n+1)-1)/(n+1)

p*C_(0)+p^(2)(C_(1))/(2)+p^(3)(C_(2))/(3)+...+p^(n+1)*(C_(n))/(n+1)=((p+1)^(n+1)-1)/(n+1)

C_ (0) ^ (2) + 2C_ (1) ^ (2) + 3.C_ (2) ^ (2) + ............ + (n + 1) C_ (n ) ^ (2) =