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69.quad (C(1))/(C(0))+2(C(2))/(C(1))+3(C...

69.quad (C_(1))/(C_(0))+2(C_(2))/(C_(1))+3(C_(3))/(C_(2))+...++n(C_(n))/(C_(n))

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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)

(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)

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

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

(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))^(2)+2(C_(1))^(2)+3(C_(2))^(2)+4(C_(3))^(2)...+(n+1)(c_(n))^(2)