Question

 

4/ 5 * 7 + 4 / 7 * 9 + .. + 4 / 59 * 61

 

Answer 1

4/ 5 * 7 + 4 / 7 * 9 + .. + 4 / 59 * 61

= 2/5 - 2/7 + 2/7 - 2/9 + ... + 2/59 - 2/61

= 2/5 - 2/61

= 112/305

Answer 2

Đặt 

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

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

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

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

\(S=2.\frac{56}{305}=\frac{112}{305}\)