If `(1+x)^n=C_0+C_1x+C_2x^2+……..+C_nx^n`, show that `3.C_0+3^2.C_1/2+3^3.C_2/2+.+3^(n+1). C_n/(n+1)=(4^(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)

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_1x + C_2x^2 + ………. + C_n x^n , prove that : C_0 + 2C_1 + ….. + 2 ""^nC_n = 3^n

If (1+x)^n=C_0+C_1x+C_2x^2+ _____+C_nx^n, Prove that, C_1+2C_2+3C_3+_____+nC_n=n.2^(n-1) .

If (1+x)^n=C_0+C_1x+C_2x^2+…+C_nx^n show that C_1-2C_2+3C_3-4C_4+…+(-1)^(n-1) n.C_n=0 where C_r=^nC_r .

If (1+x)^n=C_0+C_1x+C_2x^2+_____+C_nx^n , prove that C_1+2C_2+3C_3+_____+ ^nC_n=n2^(n-1)

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

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