4/5 . 7 + 4/7 . 9 + ...+ 4/59 . 61
= 2 . ( 2/5 . 7 + 2/7 . 9 + ...+ 2/59 . 61 )
= 2 . ( 1/5 - 1/7 + 1/7 - 1/9 + ...+ 1/59 - 1/61 )
= 2 . ( 1/5 - 1/61 )
= 2 . 56/305
= 112/305
\(\frac{4}{5.7}+\frac{4}{7.9}+...+\frac{4}{59.61}\)
\(=\) \(2.\left(\frac{2}{5}.7+\frac{2}{7}.9+...+\frac{2}{59.61}\right)\)
\(=\) \(2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\right)\)
\(=\) \(2.\left(\frac{1}{5}-\frac{1}{61}\right)\)
\(=\) \(2.\frac{56}{305}\)
\(=\) \(\frac{112}{305}\)
