If `m` is a positive integer and `D_r=|(2r-1,\ ^m C_r,1),(m^2-1, 2^m ,m+1),(sin^2(m^2),sin^2(m),sin^2(m+1))|` . Prove that `sum_(r=0)^m D_r=0` .

Explanation

\begin{aligned}
D_{r} &=\left|\begin{array}{ccc}
2 r-1 & { }^{m} C_{r} & 1 \\
m^{2}-1 & 2^{m} & m+1 \\
\sin \left(m^{2}\right) & \sin ^{2}(m) & \sin ^{2}(m+1)
\end{array}\right| \\ \\
D_{r} &=\left|\begin{array}{ccc}
\sum_{r=0}^{m}(2 r-1) & \sum_{r=0}^{m} C_{r} & \sum_{r=0}^{m} 1 \\
...