Sửa đề: \(\left(1+\frac{1}{1\cdot3}\right)\cdot\left(1+\frac{1}{2\cdot4}\right)\cdot\left(1+\frac{1}{3\cdot5}\right)\cdot...\cdot\left(1+\frac{1}{99\cdot101}\right)\)
Ta có: \(\left(1+\frac{1}{1\cdot3}\right)\cdot\left(1+\frac{1}{2\cdot4}\right)\cdot\left(1+\frac{1}{3\cdot5}\right)\cdot...\cdot\left(1+\frac{1}{99\cdot101}\right)\)
\(=\frac{2\cdot2}{1\cdot3}\cdot\frac{3\cdot3}{2\cdot4}\cdot\frac{4\cdot4}{3\cdot5}\cdot...\cdot\frac{100\cdot100}{99\cdot101}\)
\(=\frac{2\cdot3\cdot4\cdot...\cdot100}{1\cdot2\cdot3\cdot...\cdot99}\cdot\frac{2\cdot3\cdot4\cdot...\cdot100}{3\cdot4\cdot5\cdot...\cdot101}\)
\(=100\cdot\frac{2}{101}=\frac{200}{101}\)
