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

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

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

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

If C_(r) = .^(n)C_(r) then prove that (C_(0) + C_(1)) (C_(1) + C_(2)) "….." (C_(n-1) + C_(n)) = (C_(1)C_(2)"…."C_(n-1)C_(n))(n+1)^(n)//n!