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(cos^(2)(c(1))/(c(0))+2(c(2))/(c(1))+3(c...

(cos^(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)

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

(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))

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

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

(C_(0)+C_(1))(C_(1)+C_(2))(C_(2)+C_(3))(C_(3)+C_(4)).........(C_(n-1)+C_(n))=(C_(0)C_(1)C_(2).....C_(n-1)(n+1)^(n))/(n!)