\(C=\left(\frac{1}{2-1}\right)\left(\frac{1}{3-1}\right)\left(\frac{1}{4-1}\right)...\left(\frac{1}{2022-1}\right)\)
\(\Leftrightarrow C=\frac{1}{1}\cdot\frac{1}{2}\cdot\frac{1}{3}\cdot...\cdot\frac{1}{2021}\)
\(\Leftrightarrow C=\frac{1}{1\cdot2\cdot3\cdot...\cdot2021}\)
\(C=\frac{1}{1^.2^.3^....2021}\)