Đề đúng phải là: \(B=\frac{9}{9\cdot19}+\frac{9}{19\cdot29}+\frac{9}{29\cdot39}+...+\frac{9}{2009\cdot2019}\) nhé :))
Ta có: \(B=\frac{9}{9\cdot19}+\frac{9}{19\cdot29}+\frac{9}{29\cdot39}+...+\frac{9}{2009\cdot2019}\)
\(\Rightarrow B=\frac{9}{10}\cdot\left(\frac{10}{9\cdot19}+\frac{10}{19\cdot29}+\frac{10}{29\cdot39}+...+\frac{10}{2009\cdot2019}\right)\)
\(\Rightarrow B=\frac{9}{10}\cdot\left(\frac{1}{9}-\frac{1}{19}+\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{2009}-\frac{1}{2019}\right)\)
\(\Rightarrow B=\frac{9}{10}\cdot\left(\frac{1}{9}-\frac{1}{2019}\right)=\left(\frac{9}{10}\cdot\frac{1}{9}\right)-\left(\frac{9}{10}\cdot\frac{1}{2019}\right)\)
\(\Rightarrow B=\frac{1}{10}-\frac{9}{20190}=\frac{2019}{20190}-\frac{9}{20190}=\frac{2010}{20190}=\frac{201}{2019}=\frac{67}{673}\)
Bạn kia viết đúng rùi mà.Bạn chỉ việc tách 1/19 ra thui
