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\(M=\dfrac{20}{112}+\dfrac{20}{280}+\dfrac{20}{520}+\dfrac{20}{832}\\ =\dfrac{20}{8.14}+\dfrac{20}{14.20}+\dfrac{20}{20.26}+\dfrac{20}{26.32}\\ =\dfrac{20}{6}.\left(\dfrac{6}{8.14}+\dfrac{6}{14.20}+\dfrac{6}{20.26}+\dfrac{6}{26.32}\right)\\ =\dfrac{20}{6}.\left(\dfrac{1}{8}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{32}\right)\\ =\dfrac{20}{6}.\left(\dfrac{1}{8}-\dfrac{1}{32}\right)\\ =\dfrac{20}{6}.\dfrac{3}{32}=\dfrac{5}{16}\)
Anh giải cách đây 3 ngày rồi!
\(M=\dfrac{20}{112}+\dfrac{20}{280}+\dfrac{20}{520}+\dfrac{20}{832}\\ M=\dfrac{20}{8.14}+\dfrac{20}{14.20}+\dfrac{20}{20.26}+\dfrac{20}{26.32}\\ M=\dfrac{20}{6}\left(\dfrac{6}{8.14}+\dfrac{6}{14.20}+\dfrac{6}{20.26}+\dfrac{6}{26.32}\right)\\M=\dfrac{20}{6}\left(\dfrac{1}{8}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{32}\right)\\ M=\dfrac{20}{6}\left(\dfrac{1}{8}-\dfrac{1}{32}\right)=\dfrac{20}{6}.\dfrac{3}{32}=\dfrac{5}{16}\)
\(M=\dfrac{20}{112}+\dfrac{20}{280}+\dfrac{20}{520}+\dfrac{20}{832}\)
\(\Rightarrow M=\dfrac{20}{8.14}+\dfrac{20}{14.20}+\dfrac{20}{20.26}+\dfrac{20}{26.32}\)
\(\Rightarrow M=\dfrac{20}{6}\left(\dfrac{6}{8.14}+\dfrac{8}{14.20}+\dfrac{8}{20.26}+\dfrac{8}{26.32}\right)\)
\(\Rightarrow M=\dfrac{20}{6}\left(\dfrac{1}{8}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{32}\right)\)
\(\Rightarrow M=\dfrac{20}{6}\left(\dfrac{1}{8}-\dfrac{1}{32}\right)\)
\(\Rightarrow M=\dfrac{20}{6}.\dfrac{3}{32}=\dfrac{5}{16}\)
Bài 1: Ta có:
\(M=\dfrac{20}{112}+\dfrac{20}{280}+\dfrac{20}{520}+\dfrac{20}{832}\)
\(=\dfrac{20}{8.14}+\dfrac{20}{14.20}+\dfrac{20}{20.26}+\dfrac{20}{26.32}\)
\(=\dfrac{20}{6}\left(\dfrac{6}{8.14}+\dfrac{6}{14.20}+\dfrac{6}{20.26}+\dfrac{6}{26.32}\right)\)
\(=\dfrac{20}{6}\left(\dfrac{1}{8}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{20}+...+\dfrac{1}{26}-\dfrac{1}{32}\right)\)
\(=\dfrac{20}{6}\left(\dfrac{1}{8}-\dfrac{1}{32}\right)=\dfrac{20}{6}.\dfrac{3}{32}=\dfrac{5}{16}\)
Vậy \(M=\dfrac{5}{16}\)
Bài 2: Ta có:
\(A=\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}+...+\dfrac{1}{210}\)
\(=\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}+...+\dfrac{1}{14.15}\)
\(=\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{14}-\dfrac{1}{15}\)
\(=\dfrac{1}{6}-\dfrac{1}{15}=\dfrac{1}{10}\)
Vậy \(A=\dfrac{1}{10}\)
Giải:
\(M=\dfrac{20}{112}+\dfrac{20}{280}+\dfrac{20}{520}+\dfrac{20}{832}.\)
\(M=\dfrac{5}{28}+\dfrac{5}{70}+\dfrac{5}{130}+\dfrac{5}{208}.\)
\(M=\dfrac{5}{4.7}+\dfrac{5}{7.10}+\dfrac{5}{10.13}+\dfrac{5}{13.16}.\)
\(M=\dfrac{5}{3}\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}\right).\)
\(M=\dfrac{5}{3}\left[\left(\dfrac{1}{7}-\dfrac{1}{7}\right)+\left(\dfrac{1}{10}-\dfrac{1}{10}\right)+\left(\dfrac{1}{13}-\dfrac{1}{13}\right)+\left(\dfrac{1}{4}-\dfrac{1}{16}\right)\right].\)
\(M=\dfrac{5}{3}\left[0+0+0+\left(\dfrac{1}{4}-\dfrac{1}{16}\right).\right]\)
\(M=\dfrac{5}{3}\left(\dfrac{1}{4}-\dfrac{1}{16}\right).\)
\(M=\dfrac{5}{3}\left(\dfrac{4}{16}-\dfrac{1}{16}\right).\)
\(M=\dfrac{5}{3}.\dfrac{3}{16}.\)
\(M=\dfrac{15}{48}=\dfrac{5}{16}.\)
M=20/8.14+20/14.20+20/20.26+20/26.32
=>M=20/6(6/8.14+6/14.20+6/20.26+6/26.32)
=>M=20/6(1/8-1/14+1/14-1/20+1/20-1/26+1/26-1/32)
=>M=20/6(1/8-1/32)
= 20/6.3/32
=5/16
\(M=\frac{20}{112}+\frac{20}{280}+\frac{20}{520}+\frac{20}{832}\)
\(M=\frac{20}{8.14}+\frac{20}{14.20}+\frac{20}{20.26}+\frac{20}{26.32}\)
\(M=\frac{20}{6}.\left(\frac{6}{8.14}+\frac{6}{14.20}+\frac{6}{20.26}+\frac{6}{26.32}\right)\)
\(M=\frac{20}{6}\left(\frac{1}{8}-\frac{1}{14}+\frac{1}{14}-\frac{1}{20}+\frac{1}{20}-\frac{1}{26}+\frac{1}{26}-\frac{1}{32}\right)\)
\(M=\frac{20}{6}\left(\frac{1}{8}-\frac{1}{32}\right)\)
\(M=\frac{20}{6}\cdot\frac{3}{32}\)
\(M=\frac{5}{16}\)
$M=\frac{20}{112}+\frac{20}{280}+\frac{20}{520}+\frac{20}{832}$
$M=\frac{20}{8.14}+\frac{20}{14.20}+\frac{20}{20.26}+\frac{20}{26.32}$
$M=\frac{20}{6}.\left(\frac{6}{8.14}+\frac{6}{14.20}+\frac{6}{20.26}+\frac{6}{26.32}\right)$
$M=\frac{20}{6}\left(\frac{1}{8}-\frac{1}{14}+\frac{1}{14}-\frac{1}{20}+\frac{1}{20}-\frac{1}{26}+\frac{1}{26}-\frac{1}{32}\right)$
$M=\frac{20}{6}\left(\frac{1}{8}-\frac{1}{32}\right)$
$M=\frac{20}{6}\cdot \frac{3}{32}$
$M=\frac{5}{16}$
\(M=\dfrac{20}{112}+\dfrac{20}{180}+\dfrac{20}{520}+\dfrac{20}{832}\)
\(M=\dfrac{20}{8.14}+\dfrac{20}{14.20}+\dfrac{20}{20.26}+\dfrac{20}{26.32}\)
\(M=\dfrac{20}{6}\left(\dfrac{6}{8.14}+\dfrac{6}{14.20}+\dfrac{6}{20.26}+\dfrac{6}{26.32}\right)\)
\(M=\dfrac{20}{6}\left(\dfrac{1}{8}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{32}\right)\)
\(M=\dfrac{20}{6}\left(\dfrac{1}{8}-\dfrac{1}{32}\right)\)
\(M=\dfrac{20}{6}.\dfrac{3}{32}\)
\(M=\dfrac{5}{16}\)
\(M=\dfrac{20}{8.14}+\dfrac{20}{14.20}+....+\dfrac{20}{26.32}\)
\(M=\dfrac{20}{6}.\left(\dfrac{1}{8}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{20}+.....+\dfrac{1}{26}-\dfrac{1}{32}\right)\)
\(M=\dfrac{20}{6}.\left(\dfrac{1}{8}-\dfrac{1}{32}\right)\)=\(\dfrac{20}{6}.\dfrac{3}{32}=\dfrac{5}{16}\)
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