a) \(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{99}\right)\cdot\left(1-\frac{1}{100}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{98}{99}\cdot\frac{99}{100}\)
\(=\frac{1\cdot2\cdot3\cdot...\cdot98\cdot99}{2\cdot3\cdot4\cdot...\cdot99\cdot100}=\frac{1}{100}\)
b) \(\left(1+\frac{1}{2}\right)\cdot\left(1+\frac{1}{3}\right)\cdot\left(1+\frac{1}{4}\right)\cdot...\cdot\left(1+\frac{1}{99}\right)\cdot\left(1+\frac{1}{100}\right)\)
\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{100}{99}\cdot\frac{101}{100}\)
\(=\frac{3\cdot4\cdot5\cdot...\cdot100\cdot101}{2\cdot3\cdot4\cdot...\cdot99\cdot100}=\frac{101}{2}\)
