If `(1+x)^n=c_0+C_1x+C_2x^2++C_n x^n `,using derivative prove that `C_1+2C_2++nC_n=n .2^(n-1)` `C_1-2C_2+3C_3++(-1)^(n-1)nC_n=0`

If (1+x)^(n)=c_(0)+C_(1)x+C_(2)x^(2)++C_(n)x^(n) ,using derivative prove that C_(1)+2C_(2)++nC_(n)=n.2^(n-1)C_(1)-2C_(2)+3C_(3)++(-1)^(n-1)nC_(n)=0

If (1+x)^n=c_0+C_1x+C_2x^2++C_n x^n , using derivtives prove t h a t C_1-2C_2+3C_3++(-1)^(n-1)nC_n=0

If (1+x)^n=c_0+C_1x+C_2x^2++C_n x^n , using derivtives prove t h a t C_1-2C_2+3C_3++(-1)^(n-1)nC_n=0

If (1+x)^(n)=C_(0)+C_(1)+C_(2)x^(2)++C_(n)x^(n) using derivatives prove that C_(1)+2C_(2)++nC_(n)=n.2^(n-1)(ii)C_(1)-2C_(2)+3C_(3)++(-1)^(n-1)nC_(n)=0

C_0 - [C_1 -2.C_2+ 3.C_3-……..+(-1)^(n-1).n.C_n] =

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 , then prove that : C_1 -2C_2+………….+(-1)^(n-1)nC_n =0

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_1 x+ C_2 x^2 +....... C_nx^n prove that : C_0+ 2C_1 +.........+2""^nC_n=3^n .