Question

Thực hiện phép tính :

b) \(\frac{5}{4\times6}\)+ \(\frac{5}{6\times8}\)+ \(\frac{5}{8\times10}\)+ ... + \(\frac{5}{298\times300}\)

Answer 1

\(\frac{5}{4.6}+\frac{5}{6.8}+\frac{5}{8.10}+....+\frac{5}{298.300}\)

\(=\frac{5}{2}.\left(\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+....+\frac{2}{298.300}\right)\)

\(=\frac{5}{2}.\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+....+\frac{1}{298}-\frac{1}{300}\right)\)

\(=\frac{5}{2}.\left(\frac{1}{4}-\frac{1}{300}\right)=\frac{5}{2}.\frac{37}{150}=\frac{37}{60}\)

Vậy..........