Prove that `(C_0+C_1)(C_1+C_2)(C_2+C_3)(C_(n-1)+C_n)=(n+1)^n/(n!).c_0.C_1.C_2...........C_n`.

( (C_0 +C_1)(C_1 + C_2)(C_2 +C_3).....(C_(n-1) +C_n))/(C_0C_1C_2....C_n)= (A) (n+1) ^n/n (B) (n+1)^(n-1)/n! (C) (n+1)^n/(n!)(D) (n+1)/(n!)

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

Prove that : C_(0)-3C_(1)+5C_(2)- ………..(-1)^n(2n+1)C_(n)=0

Prove that C_(0)^(2)+C_(1)^(2)+...C_(n)^(2)=(2n!)/(n!n!)

prove that C_(0)C_(n)+C_(1)C_(n-1)+C_(2)C_(n-2)+.........+C_(n)C_(0)=2nC_(n)