Question

giai bài S= 4/5.7+4/7.9+...+4/59.61

 

​

​

Answer 1

Ta có:

\(S=\frac{4}{5.7}+\frac{4}{7.9}+\frac{4}{9.11}+...+\frac{4}{59.61}\)

\(=2.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)

\(=2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\right)\)

\(=2.\left(\frac{1}{5}-\frac{1}{61}\right)\)

\(=2.\left(\frac{61}{305}-\frac{5}{305}\right)\)

\(=2.\frac{56}{305}\)

\(=\frac{112}{305}\)

Vậy \(S=\frac{112}{305}\)