[" ((ii)) Prove that "],[qquad (C_(1))/(C_(0))+(2C_(2))/(C_(1))+(3C_(3))/(C_(3))+.....(nC_(n))/(C_(n-1))=(n(n+1))/(2)]

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

Prove that : Prove that (C_(1))/(C_(0))+2.(C_(2))/(C_(1))+3.(C_(3))/(C_(2))+….+n.(C_(n))/(C_(n-1))=(n(n+1))/(2)

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

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

If (1+x)^(n)=C_(0)+C_(1)x+…..+C_(n)x^(n) , then (C_(1))/(C_(0))+(2C_(2))/(C_(1))+(3C_(3))/(C_(2))+....+(nC_(n))/(C_(n-1)) is :

If (1+x)^(n)=C_(0)+C_(1)x+…..+C_(n)x^(n) , then (C_(1))/(C_(0))+(2C_(2))/(C_(1))+(3C_(3))/(C_(2))+....+(nC_(n))/(C_(n-1)) is :

C_1/C_0 + (2C_2)/C_1 + (3C_3)/C_2 + .... (nC_n)/C_(n-1) is

Prove that (C_(1))/(1)-(C_(2))/(2)+(C_(3))/(3)-(C_(4))/(4)+...+((-1)^(n-1))/(n)C_(n)=1+(1)/(2)+(1)/(3)+...+(1)/(n)

c_(1)^(2)+2C_(2)^(2)+3C_(3)^(2)+....+nC_(n)^(2)=((2n-1)!)/ ([(n-1)!^(2)))

C_1/C_0+2C_2/C_1+3C_3/C_2+............+nC_n/C_(n-1)=(n(n+1))/2