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

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(0))/(1)-(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)

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

Prove that C_1/C_0+(2c_(2))/C_1+(3C_3)/(C_2)+......+(n.C_n)/(C_(n-1))=(n(n+1))/2

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

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) .

Prove that (i) C_(1)+2C_(2)+3C_(3)+……+nC_(n)=n.2^(n-1) (ii) C_(0)+(C_(1)/(2)+(C_(2))/(3)+….+(C_(n))/(n+1)=(2^(n+1)-1)/(n+1)