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15 tháng 12 2016
Ta có: 1/2=1/1*2 m*m+1=n
Nên 1/1*2 + 1/2*3 + 1/3*4 +... +1/m*m+1
(1-1/2) + (1/2-1/3) + ... (1/m-1/m+1)
Triệt tiêu đi còn1- 1/m+1 =39/40
Suy ra 1/m+1 = 1/40
Vậy m=39
n = 39* (39+1) = 39*40= 1560
HN
2
31 tháng 7 2019
\(\left(\times-\frac{1}{5}\right):\left(\frac{1}{2}+\frac{1}{6}+\cdot\cdot\cdot+\frac{1}{110}\right)=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right):\left(\frac{1}{1\times2}+\cdot\cdot\cdot+\frac{1}{10\times11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right):\left(1-\frac{1}{2}+\cdot\cdot\cdot+\frac{1}{10}-\frac{1}{11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right):\left(1-\frac{1}{11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right):\frac{10}{11}=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right)=\frac{1}{5}\times\frac{10}{11}\)
\(\Rightarrow\times-\frac{1}{5}=\frac{2}{11}\)
\(\Rightarrow\times=\frac{2}{11}+\frac{1}{5}\)
\(\Rightarrow\times=\frac{21}{55}\)
XO
31 tháng 7 2019
\(\left(x-\frac{1}{5}\right):\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)=\frac{1}{5}\)
\(\Rightarrow\left(x-\frac{1}{5}\right):\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{10\times11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(x-\frac{1}{5}\right):\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(x-\frac{1}{5}\right):\left(1-\frac{1}{11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(x-\frac{1}{5}\right):\frac{10}{11}=\frac{1}{5}\)
\(\Rightarrow x-\frac{1}{5}=\frac{1}{5}\times\frac{10}{11}\)
\(\Rightarrow x-\frac{1}{5}=\frac{2}{11}\)
\(\Rightarrow x=\frac{2}{11}+\frac{1}{5}\)
\(\Rightarrow x=\frac{21}{55}\)
Vậy \(x=\frac{21}{55}\)
2 tháng 6 2017
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}+\frac{1}{132}\)
= \(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{10\times11}+\frac{1}{11\times12}\)
= \(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)
= \(\frac{1}{1}-\frac{1}{12}\)
= \(\frac{11}{12}\)
2 tháng 6 2017
Ta có : \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+......+\frac{1}{132}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+......+\frac{1}{11.12}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{11}-\frac{1}{12}\)
\(=1-\frac{1}{12}\)
\(=\frac{11}{12}\)
28 tháng 4 2019
\(\left(y-\frac{1}{2}\right):\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)=\frac{1}{3}\)
=> \(\left(y-\frac{1}{2}\right):\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)=\frac{1}{3}\)
=> \(\left(y-\frac{1}{2}\right):\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)=\frac{1}{3}\)
=> \(\left(y-\frac{1}{2}\right):\left(1-\frac{1}{10}\right)=\frac{1}{3}\)
=> \(\left(y-\frac{1}{2}\right):\frac{9}{10}=\frac{1}{3}\)
=> \(y-\frac{1}{2}=\frac{3}{10}\)
=> \(y=\frac{13}{10}\)
Study well ! >_<
28 tháng 10 2018
\(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{90}=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{9\cdot10}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{1}-\frac{1}{10}=1-\frac{1}{10}=\frac{9}{10}\)
7 tháng 7 2019
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}-\frac{1}{7}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{1}-\frac{1}{10}=\frac{9}{10}\)
A
0
NN
13 tháng 6 2020
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}=1-\frac{1}{6}=\frac{5}{6}\)
DP
23 tháng 6 2017
\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)\div x=\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{32}\right)\)
\(\left(\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}\right)\div x=\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{11.12}\right)\)
\(\frac{15}{16}\div x=\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{12}\right)\)
\(\frac{15}{16}\div x=\left(\frac{1}{1}-\frac{1}{12}\right)\)
\(\frac{15}{16}\div x=\frac{11}{12}\)
\(x=\frac{15}{16}\div\frac{11}{12}\)
\(x=\frac{15}{16}\times\frac{12}{11}\)
\(\Rightarrow x=\frac{180}{176}=\frac{45}{44}\)
\(M=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{20.21}\)
\(M=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-....-\frac{1}{20}+\frac{1}{20}-\frac{1}{21}\)
\(M=1-\frac{1}{21}\)
\(M=\frac{20}{21}\)
\(M=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{420}\)
\(M=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{20.21}\)
\(M=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{20}-\frac{1}{21}\)
\(M=1-\frac{1}{21}\)
\(M=\frac{20}{21}\)