Question

[Linh Trần]

Tính:

M = \(\frac{20}{112}\) \(+\) \(\frac{20}{280}+\frac{20}{520}+\frac{20}{832}\)

Answer 1

[Võ Đông Anh Tuấn]

\(M=\frac{20}{112}+\frac{20}{280}+\frac{20}{520}+\frac{20}{832}\)

\(M=\frac{20}{8.14}+\frac{20}{14.20}+\frac{20}{20.26}+\frac{20}{26.32}\)

\(M=\frac{20}{6}.\left(\frac{6}{8.14}+\frac{6}{14.20}+\frac{6}{20.26}+\frac{6}{26.32}\right)\)

\(M=\frac{20}{6}.\left(\frac{1}{8}-\frac{1}{14}+\frac{1}{14}-\frac{1}{20}+\frac{1}{20}-\frac{1}{26}+\frac{1}{26}-\frac{1}{32}\right)\)

\(M=\frac{20}{6}.\left(\frac{1}{8}-\frac{1}{32}\right)\)

\(M=\frac{20}{6}.\frac{3}{32}\)

\(M=\frac{5}{16}\)

Answer 2

[Nguyễn Trần An Thanh]

\(M=\frac{20}{112}+\frac{20}{280}+\frac{20}{520}+\frac{20}{832}\)

\(\Rightarrow\frac{1}{M}=\frac{112}{20}+\frac{280}{20}+\frac{520}{20}+\frac{832}{20}\)

\(\Rightarrow\frac{1}{M}=\frac{1744}{20}=\frac{436}{5}\)

\(\Rightarrow M=\frac{5}{436}\)