Question

Tính nhanh:

\(\frac{4}{2.4}+\frac{4}{4.6}+...+\frac{4}{98.100}\)

Answer 1

\(\frac{4}{2.4}+\frac{4}{4.6}+...+\frac{4}{98.100}\)

\(=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=2.\frac{49}{100}\)

\(=\frac{49}{50}\)

Answer 2

\(=2\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{98.100}\right)\)

\(=2\cdot\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right)\)

\(=2\cdot\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=2\cdot\frac{49}{100}\)

\(=\frac{49}{50}\)