If `m in N` and `mgeq2` prove that: `|1 1 1\ ^m C_1\ ^(m+1)C_1\ ^(m+2)C_1\ ^m C_2\ ^(m+1)C_2\ ^(m+2)C_2|=1` .

Answer

Proved

Explanation

$$
\left|\begin{array}{ccc}
1 & 1 & 1 \\
{ }^{m} C_{1} & { }^{\mathrm{m}+1} C_{1} & { }^{m+2} C_{1} \\
{ }^{m} C_{2} & { }^{m+1} C_{2} & { }^{m+2} C_{2}
\end{array}\right|=\left|\begin{array}{ccc}
1 & 1 & 1 \\
{ }^{m} C_{1} & { }^{m+1} C_{1} & { }^{m+1} C_{0}+{ }^{m+1} C_{1} \\
...