Question

Tính nhanh: \(\frac{25}{72}+\frac{25}{90}+\frac{25}{110}+\frac{25}{132}+...+\frac{25}{9900}\)

Answer 1

\(\frac{25}{72}+\frac{25}{90}+\frac{25}{110}+...+\frac{25}{9900}\)

= \(25.\left(\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+...+\frac{1}{9900}\right)\)

= \(25.\left(\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+...+\frac{1}{99.100}\right)\)

= \(25.\left(\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+...+\frac{1}{99}-\frac{1}{100}\right)\)

= \(25.\left(\frac{1}{8}-\frac{1}{100}\right)\)

= \(25.\frac{23}{200}\)

= \(\frac{23}{8}\)