Anh giải cách đây 3 ngày rồi!
\(M=\dfrac{20}{112}+\dfrac{20}{280}+\dfrac{20}{520}+\dfrac{20}{832}\\ M=\dfrac{20}{8.14}+\dfrac{20}{14.20}+\dfrac{20}{20.26}+\dfrac{20}{26.32}\\ M=\dfrac{20}{6}\left(\dfrac{6}{8.14}+\dfrac{6}{14.20}+\dfrac{6}{20.26}+\dfrac{6}{26.32}\right)\\M=\dfrac{20}{6}\left(\dfrac{1}{8}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{32}\right)\\ M=\dfrac{20}{6}\left(\dfrac{1}{8}-\dfrac{1}{32}\right)=\dfrac{20}{6}.\dfrac{3}{32}=\dfrac{5}{16}\)
\(M=\dfrac{20}{112}+\dfrac{20}{280}+\dfrac{20}{520}+\dfrac{20}{832}\)
\(\Rightarrow M=\dfrac{20}{8.14}+\dfrac{20}{14.20}+\dfrac{20}{20.26}+\dfrac{20}{26.32}\)
\(\Rightarrow M=\dfrac{20}{6}\left(\dfrac{6}{8.14}+\dfrac{8}{14.20}+\dfrac{8}{20.26}+\dfrac{8}{26.32}\right)\)
\(\Rightarrow M=\dfrac{20}{6}\left(\dfrac{1}{8}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{32}\right)\)
\(\Rightarrow M=\dfrac{20}{6}\left(\dfrac{1}{8}-\dfrac{1}{32}\right)\)
\(\Rightarrow M=\dfrac{20}{6}.\dfrac{3}{32}=\dfrac{5}{16}\)
\(M=\dfrac{20}{112}+\dfrac{20}{280}+\dfrac{20}{520}+\dfrac{20}{832}\)
\(M=\dfrac{20}{8.14}+\dfrac{20}{14.20}+\dfrac{20}{20.26}+\dfrac{20}{26.32}\)
\(M=\dfrac{20}{6}.\left(\dfrac{20}{8.14}+\dfrac{20}{14.20}+\dfrac{20}{20.26}+\dfrac{20}{26.32}\right)\)
\(M=\dfrac{20}{6}.\left(\dfrac{1}{8}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{32}\right)\)
(do \(\dfrac{n}{a.\left(a+n\right)}=\dfrac{1}{a}-\dfrac{1}{a+n}\) với \(a\in N\)*)
\(M=\dfrac{20}{6}.\left(\dfrac{1}{8}-\dfrac{1}{32}\right)=\dfrac{6}{20}.\dfrac{3}{32}=\dfrac{5}{16}\)
Chúc bạn học tốt!!!
\(M=\dfrac{20}{112}+\dfrac{20}{280}+\dfrac{20}{520}+\dfrac{20}{832}\)
\(=\dfrac{20}{8\cdot14}+\dfrac{20}{14\cdot20}+\dfrac{20}{20\cdot26}+\dfrac{20}{26\cdot32}\)
\(=\dfrac{10}{3}\left(\dfrac{6}{8\cdot14}+\dfrac{6}{14\cdot20}+\dfrac{6}{20\cdot26}+\dfrac{6}{26\cdot32}\right)\)
\(=\dfrac{10}{3}\left(\dfrac{1}{8}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{32}\right)\)
\(=\dfrac{10}{3}\left(\dfrac{1}{8}-\dfrac{1}{32}\right)\)
\(=\dfrac{10}{3}\left(\dfrac{4}{32}-\dfrac{1}{32}\right)\)
\(=\dfrac{10}{3}\cdot\dfrac{3}{32}\)
\(=\dfrac{5}{16}\)