Prove that `(""^(2n)C_(0))^2-(""^(2n)C_(1))^2+(""^(2n)C_(2))^2-.....+(-1)^n(""^(2n)C_(2n))^2=(-1)^n.""^(2n)C_(n)`

Prove that (""^(2n)C_(0))^(2)-(""^(2n)C_(1))^(2)+(""^(2n)C_(2))^(2)-…+(""^(2n)C_(2n))^(2)=(-1)^(n)*""^(2n)C_(n) .

Prove that (""^(2n)C_(0))^(2)-(""^(2n)C_(1))^(2)+(""^(2n)C_(2))-(""^(2n)C_(3))^(2)+......+(""^(2n)C_(2n))^(2)=(-1)^(n)(""^(2n)C_(n))^2.

Prove that (^(2n)C_0)^2-(^(2n)C_1)^2+(^(2n)C_2)^2-+(^(2n)C_(2n))^2-(-1)^n^(2n)C_ndot

Prove that (^(2n)C_0)^2+(^(2n)C_1)^2+(^(2n)C_2)^2-+(^(2n)C_(2n))^2-(-1)^n^(2n)C_ndot

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

""^(2n +1)C_0^2 -""^(2n+1)C_1^2 + ""^(2n+1)C_2^2 -…….- ""^(2n+1)C_(2n+1)^2 =

""^(2n)C_(n+1)+2. ""^(2n)C_(n) + ""^(2n) C_(n-1) =

Prove that (C_(0) +C_(1)+C_(2)+….+C_(n))^(2)=1 +""^(2n)C_(1) +""^(2n)C_(2) +…..+""^(2n)C_(2n)

Prove that "^(2n)C_0 + ^(2n)C_2 + .... + ^(2n)C_(2n) = 2^(2n-1)