Theo đầu bài ta có:
\(\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)...\left(1-\frac{1}{199^2}\right)\left(1-\frac{1}{200^2}\right)\)
\(=\frac{1\cdot3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\frac{3\cdot5}{4\cdot4}\cdot...\cdot\frac{198\cdot200}{199\cdot199}\cdot\frac{199\cdot201}{200\cdot200}\)
\(=\frac{1}{2}\cdot\frac{201}{200}=\frac{201}{400}\)