Ta có :
\(M=\dfrac{20}{112}+\dfrac{20}{280}+\dfrac{20}{520}+\dfrac{20}{832}\)
\(M=\dfrac{20}{8\times14}+\dfrac{20}{14\times20}+\dfrac{20}{20\times26}+\dfrac{20}{26\times32}\)
\(\Rightarrow\dfrac{3}{10}M=\dfrac{6}{8\times14}+\dfrac{6}{14\times20}+\dfrac{6}{20\times26}+\dfrac{6}{26\times32}\)
\(\dfrac{3}{10}M=\dfrac{1}{8}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{32}\)
\(\dfrac{3}{10}M=\dfrac{1}{8}-\dfrac{1}{32}=\dfrac{3}{32}\)
\(\Rightarrow M=\dfrac{3}{32}\div\dfrac{3}{10}=\dfrac{5}{16}\)
\(M=\dfrac{20}{112}+\dfrac{20}{280}+\dfrac{20}{520}+\dfrac{20}{832}\)
\(M=20.\left(\dfrac{1}{112}+\dfrac{1}{280}+\dfrac{1}{520}+\dfrac{1}{832}\right)\)
\(M=20.\left(\dfrac{1}{8.14} +\dfrac{1}{14.20}+\dfrac{1}{20.26}+\dfrac{1}{26.32}\right)\)
\(\Rightarrow6M=20.\left(\dfrac{6}{8.14}+\dfrac{6}{14.20}+\dfrac{6}{20.26}+\dfrac{6}{26.32}\right)\)
\(\Rightarrow6M=20.\left(\dfrac{1}{8}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{32}\right)\)
\(\Rightarrow6M=20.\left(\dfrac{1}{8}-\dfrac{1}{32}\right)\)
\(\Rightarrow6M=20.\dfrac{3}{32}\)
\(\Rightarrow6M=\dfrac{15}{8}\)
\(\Rightarrow M=\dfrac{15}{8}:6\)
\(\Rightarrow M=\dfrac{5}{16}\)
Vậy \(M=\dfrac{5}{16}\)
\(M=\dfrac{20}{112}+\dfrac{20}{280}+\dfrac{20}{520}+\dfrac{20}{832}\)
\(M=20\left(\dfrac{1}{112}+\dfrac{1}{280}+\dfrac{1}{520}+\dfrac{1}{832}\right)\)
\(M=20\left(\dfrac{1}{8\cdot14}+\dfrac{1}{14\cdot20}+\dfrac{1}{20\cdot26}+\dfrac{2}{26\cdot32}\right)\)
Đặt \(N=\dfrac{1}{8\cdot14}+\dfrac{1}{14\cdot20}+\dfrac{1}{20\cdot26}+\dfrac{1}{26\cdot32}\)
\(6N=\dfrac{1}{8}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{32}\)
\(N=\left(\dfrac{1}{8}-\dfrac{1}{32}\right):6=\dfrac{1}{64}\)
\(M=20\cdot\dfrac{1}{64}=\dfrac{5}{16}\)
