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C0/(1.2)+C1/(2.3)+C2/(3.4)+........Cn/((...

`C_0/(1.2)+C_1/(2.3)+C_2/(3.4)+........C_n/((n+1)(n+ 2))=`

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Show that (2^(2) *C_(0) )/(1*2)+(2^(3)*C_(1))/(2*3)+(2^(4) *C_(2))/(3*4)+…+(2^(n+2)*C_(n))/((n+1)(n+2)) = (3^(n+2) - 2n-5)/((n+1)(n+2)) Hence deduce that (C_(0))/(1.2) -(C_(1))/(2.3) +(C_(2))/(3.4) -…=(1)/(n+2)

(2^(2)*c_(0))/(1.2)+(2^(3)*C_(1))/(2.3)+(2^(4)*c_(2))/(3.4)+......+(2^(n+2)*C_(n))/((n+1)(n+2))=

(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!)

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

Prove that C_0+(C_1)/(2)+(C_2)/(3)+....+(C_n)/(n+1)=(2^(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_0C_1C_2.....C_(n-1) (n+1)^n)/(n!)

Prove that (C_0+C_1)(C_1+C_2)(C_2+C_3)(C_3+C_4)...........(C_(n-1)+C_n) = (C_0C_1C_2.....C_(n-1)(n+1)^n)/(n!)