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\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)
\(S=1-\frac{1}{9}=\frac{8}{9}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{2}:\frac{3}{2}:\frac{5}{4}:\frac{6}{5}:\frac{7}{6}:\frac{8}{7}\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\)
\(=\frac{1\cdot\left(2\cdot5\cdot6\cdot7\right)}{8\cdot3\cdot\left(2\cdot5\cdot6\cdot7\right)}\)
\(=\frac{1}{24}\)
\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\cdot\frac{8}{9}\cdot\frac{9}{10}\)
\(=\frac{1\cdot\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)}{\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)\cdot10}\)
\(=\frac{1}{10}\)
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Bài 1 :
A = 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + ... + 1/32 - 1/64
A = 1 - 1/64
A = 63/64
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\(\frac{4}{9}x\frac{3}{7}+\frac{5}{7}x\frac{4}{9}-\frac{4}{9}x\frac{1}{7}\)
\(=\frac{4}{9}x\left(\frac{3}{7}+\frac{5}{7}-\frac{1}{7}\right)\)
\(=\frac{4}{9}\)
\(\frac{4}{9}\times\frac{3}{7}+\frac{5}{7}\times\frac{4}{9}-\frac{4}{9}\times\frac{1}{7}\)
\(=\frac{4}{9}\times\left(\frac{3}{7}+\frac{5}{7}-\frac{1}{7}\right)\)
\(=\frac{4}{7}\times1\)
\(=\frac{4}{7}\)
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\(\frac{25}{32}\cdot\frac{8}{50}.\frac{4}{3}.\frac{5}{10}=\frac{1}{12}\)
\(\frac{25}{32}\times\frac{8}{50}\times\frac{4}{3}\times\frac{5}{10}\)
\(=\frac{5\times5\times8\times4\times5}{8\times4\times5\times5\times2\times3\times5\times2}\)
\(=\frac{1}{12}\)
k mk nha
thank you very much
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\(\dfrac{18}{3}=18:3=6\)
\(\dfrac{45}{9}=45:9=5\)
\(\dfrac{8}{8}=8:8=1\)
\(\dfrac{7}{1}=7:1=7\)
![](https://rs.olm.vn/images/avt/0.png?1311)
<=>4/7+x=5/8
<=>x=3/56
\(\frac{4}{7}+x=\frac{7}{8}-\frac{1}{4}\)
\(\frac{4}{7}+x=\frac{5}{8}\)
\(x=\frac{5}{8}-\frac{4}{7}\)
\(x=\frac{3}{56}\)