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

(C_(0))/(1*2)+(C_(1))/(2*3)+(C_(2))/(3*4)+...+(C_(n))/((n+1)(n+2))=

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

(C_(0))/(1.2)+(C_(1))/(2.3)+(C_(2))/(3.4)+......*(C_(n))/((n+1)(n+2))=

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)

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)

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)

Prove the following: C_(0)-(C_(1))/(2)+(C_(2))/(3) - …+(-1)^(n)(C_(n))/(n+1)=(1)/(n+1)

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

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