Tính:
1. \(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)...\left(1-\dfrac{1}{100}\right)\)
\(=\left(\dfrac{2}{2}-\dfrac{1}{2}\right)\left(\dfrac{3}{3}-\dfrac{1}{3}\right)...\left(\dfrac{100}{100}-\dfrac{1}{100}\right)\)
\(=\dfrac{1}{2}.\dfrac{2}{3}...\dfrac{99}{100}\)
\(=\dfrac{1}{100}\)
\(\Rightarrow\dfrac{1}{100}\)
2. \(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{98.100}\)
\(=\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{98}-\dfrac{1}{100}\right)\)
\(=\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{100}\right)\)
\(=\dfrac{1}{2}.\left(\dfrac{50}{100}-\dfrac{1}{100}\right)\)
\(=\dfrac{1}{2}.\dfrac{49}{100}\)
\(=\dfrac{49}{200}\)
\(\Rightarrow\dfrac{49}{200}\)
