Đặt A là tên của biểu thức trên
2A = \(\frac{7.2}{5.9}+\frac{7.2}{9.11}+\frac{7.2}{11.13}+\frac{7.2}{13.15}+...+\frac{7.2}{2015.2017}\)
2A = \(7\left(\frac{2}{5.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{2015.2017}\right)\)
2A = \(7\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{2015}-\frac{1}{2017}\right)\)
2A = \(7\left(\frac{1}{5}-\frac{1}{2017}\right)\)
2A = \(7\cdot\frac{2012}{10085}\)
2A = \(\frac{14084}{10085}\)
A = \(\frac{14084}{10085}:2\)
A = \(\frac{7042}{10085}\)
\(\frac{7}{5.9}+\frac{7}{9.11}+\frac{7}{11.13}+\frac{7}{11.13}+...+\frac{7}{2015.2017}\)
\(=\frac{7}{5.9}+\frac{7}{2}.\left(\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{2015.2017}\right)\)
\(=\frac{7}{45}+\frac{7}{2}.\left(\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{2015}-\frac{1}{2017}\right)\)
\(=\frac{7}{45}+\frac{7}{2}.\left(\frac{1}{9}-\frac{1}{2017}\right)\)
\(=\frac{7}{45}+\frac{7}{2}.\frac{2008}{18153}\)
=\(\frac{7}{45}+\frac{7028}{18153}\)
Đó là kết quả cuối cùng
Bỏ 7/5.9 ra ngoài, ta cộng sau nha
Còn lại: 7/9.11 + 7/11.13 + 7/13.15 +...+7/2015.2017
= 7/2 [1/9.11 + 1/11.13 + 1/13.15 +....+1/2015.2017]
= 7/2 [1/9 - 1/11 + 1/11 - 1/13 + 1/13 - 1/15 +... + 1/2015 - 1/2017]
= 7/2 [1/9 - 1/2017]
= 7/2 * 2008/18153
= 7028/18153
=> Tổng trên là: 7/45 + 7028/18153 = 14119/90765 + 35140/90765 = 49259/90765
tk nha
