Simplify `C_0^2+C_1^2/2+C_2^2/3+...+C_n^2/(n+1)`.

If (1+x)^n=C_0+C_1x+C_2x^2+……..+C_nx^n in N prove that (a) 3 C_0- 8C_1+13C_2-18C_3+...."upto" (n+1) term=0 if n ge 2 (b ) 2C_0+2^2(C_1)/(2)+2^3(C_2)/(3)+2^4C_(3)/4+....+2^(n+1)(C_n)/(n+1)=(3^n+1-1)/(n+1) ( c) C_0^2+(C_1^2)/2+C_2^2/3+....+C_n^2/(n+1)=((2n+1)!)/(((n+1)!)^2)

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

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

If (1+x)^n = C_0 + C_1x + C_2x^2 + ………. + C_n x^n , prove that : C_0 + (C_1)/(2) + (C_2)/(3) + ……. + (C_n)/(n+1) = (2^(n+1) -1)/(n+1)

If (1+x)^n =C_0+C_1 x+ C_2 x^2 +....... C_nx^n prove that : C_0+ C_1/2 +C_2/3+.........+C_n/(n+1)= (2^(n+1)-1)/(n+1) .

If (1+x)^n = C_0 + C_1 x+ C_2 x^2 + ….....+ C_n x^n, then C_0+2. C_1 +3. C_2 +….+(n+1) . C_n=