Ta có:
\(B=\frac{10}{7.12}+\frac{10}{12.17}+...+\frac{10}{2017.2022}\)
\(\Rightarrow B=2.\left(\frac{5}{7.12}+\frac{5}{12.17}+...+\frac{5}{2017.2022}\right)\)
\(\Rightarrow B=2.\left(\frac{12-7}{7.12}+\frac{17-12}{12.17}+...+\frac{2022-2017}{2017.2022}\right)\)
\(\Rightarrow B=2.\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{2017}-\frac{1}{2022}\right)\)
\(\Rightarrow B=2.\left(\frac{1}{7}-\frac{1}{2022}\right)\)
\(\Rightarrow B=\frac{2015}{7077}\)