Tính hợp lý :
M= \(\dfrac{15}{7.8}\) - \(\dfrac{17}{8.9}\) + \(\dfrac{1}{9.10}\) + \(\dfrac{1}{10.11}\)
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5 tháng 3 2017
đặt \(M=\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}\)
ta có:
\(M=\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}\)
\(\Leftrightarrow M=\dfrac{3+4}{3.4}-\dfrac{4+5}{4.5}+\dfrac{5+6}{5.6}-\dfrac{6+7}{6.7}+\dfrac{7+8}{7.8}-\dfrac{8+9}{8.9}+\dfrac{9+10}{9.10}\) \(\Leftrightarrow M=\dfrac{3}{3.4}+\dfrac{4}{3.4}-\dfrac{4}{4.5}-\dfrac{5}{4.5}+\dfrac{5}{5.6}+\dfrac{6}{5.6}-\dfrac{6}{6.7}-\dfrac{7}{6.7}+\dfrac{7}{7.8}+\dfrac{8}{7.8}-\dfrac{8}{8.9}-\dfrac{9}{8.9}+\dfrac{9}{9.10}+\dfrac{10}{9.10}\) \(\Rightarrow M=\dfrac{1}{4}+\dfrac{1}{3}-\dfrac{1}{5}-\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{5}-\dfrac{1}{7}-\dfrac{1}{6}+\dfrac{1}{8}+\dfrac{1}{7}-\dfrac{1}{9}-\dfrac{1}{8}+\dfrac{1}{10}+\dfrac{1}{9}\) \(\Rightarrow M=\dfrac{1}{3}+\dfrac{1}{10}\)
\(\Rightarrow M=\dfrac{10}{30}+\dfrac{3}{30}\)
\(\Rightarrow M=\dfrac{13}{30}\)
vậy M = \(\dfrac{13}{30}\)
vậy \(\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}=\dfrac{13}{30}\)
5 tháng 3 2017
\(\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}=\dfrac{3+4}{3.4}-\dfrac{4+5}{4.5}+\dfrac{5+6}{5.6}-\dfrac{6+7}{6.7}+\dfrac{7+8}{7.8}-\dfrac{8+9}{8.9}+\dfrac{9+10}{9.10}=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}=\dfrac{1}{3}-\dfrac{1}{10}=\dfrac{7}{30}\)
5 tháng 3 2018
\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=\dfrac{1}{2}-\dfrac{1}{10}\)
\(=\dfrac{2}{5}\)
6 tháng 4 2021
3.(1/4.5+1/5.6+...+1/9.10).x=9/2
3.(1/4-1/5+1/5-1/6+...+1/9-1/10).x=9/2
3.(1/4-1/10).x=9/2
3.3/20.x=9/2
9/20.x=9/2
x=9/2:9/20
x=10
16 tháng 4 2017
Ta có:
\(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}=1-\dfrac{1}{10}=\dfrac{9}{10}\)
\(M=\dfrac{15}{7\cdot8}-\dfrac{17}{8\cdot9}+\dfrac{1}{9\cdot10}+\dfrac{1}{10\cdot11}\)
\(M=\dfrac{1}{8}+\dfrac{1}{7}-\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}\)
\(M=\dfrac{1}{7}-\dfrac{1}{11}=\dfrac{11-7}{7\cdot11}=\dfrac{4}{77}\)
`M=15/(7.8)-17/(8.9)+1/(9.10)+1/(10.11)`
`=1/7-1/8-(1/8-1/9)+1/9-1/10+1/10-1/11`
`=1/7-1/4+2/9-1/11`
`=67/2772`
Theo mình đề bài sai phải là `M=15/(7.8)-17/(8.9)+1/(9.10)+1/(10.11)`
`=1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11`
`=1/7-1/11=4/77`