Câu 7 :
a, Tham khảo : https://olm.vn/hoi-dap/detail/43902845942.html
b, Tham khảo : https://olm.vn/hoi-dap/detail/7963533510.html
Bài 7:
b: Ta có: \(\dfrac{2}{1\cdot2}+\dfrac{2}{2\cdot3}+\dfrac{2}{3\cdot4}+...+\dfrac{2}{18\cdot19}+\dfrac{2}{19\cdot20}\)
\(=2\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{18}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{20}\right)\)
\(=2\cdot\dfrac{19}{20}=\dfrac{19}{10}\)