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\(\frac{1.5.6+2.10.12+4.20.24+9.45.54}{1.3.5+2.6.10+4.12.20+9.27.45}\)
= \(\frac{1.5.6.\left(1.1.1+2.2.2+4.4.4+9.9.9\right)}{1.3.5.\left(1.1.1+2.2.2+4.4.4+9.9.9\right)}\)
= \(\frac{1.5.6}{1.3.5}\)
= 2
\(\frac{1.5.6+2.10.12+4.20.24+9.45.54}{1.3.5+2.6.10+4.12.20+9.27.45}\)
\(=\frac{1.3.5.2+2.6.10.2+4.12.20+9.45.27.2}{1.3.5+2.6.10+4.12.20+9.45.27}\)
\(=\frac{\left(1.3.5+2.6.10+4.12.20+9.45.27\right).2}{1.3.5+2.6.10+4.12.20+9.45.27}\)
\(=2\)
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\(A=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{18\cdot19\cdot20}\)
\(A=\frac{1}{2}\cdot\frac{2}{1\cdot2\cdot3}+\frac{1}{2}\cdot\frac{2}{2\cdot3\cdot4}+\frac{1}{2}\cdot\frac{2}{3\cdot4\cdot5}+...+\frac{1}{2}\cdot\frac{2}{18\cdot19\cdot20}\)
\(A=\frac{1}{2}\left(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+...+\frac{2}{18\cdot19\cdot20}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2.3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{18\cdot19}-\frac{1}{19\cdot20}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{2}-0-0-...-0-\frac{1}{380}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{380}\right)\)
\(A=\frac{1}{2}\cdot\frac{189}{380}\)
\(A=\frac{189}{760}\)
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\(\left(\frac{136}{15}-\frac{28}{5}+\frac{62}{10}\right).\frac{21}{24}\)
\(=\left(\frac{136}{15}-\frac{28}{5}+\frac{31}{5}\right).\frac{21}{24}\)
\(=\left[\frac{136}{15}-\left(\frac{28}{5}-\frac{31}{5}\right)\right].\frac{21}{24}\)
\(=\left(\frac{136}{15}+\frac{3}{5}\right).\frac{21}{24}\)
\(=\frac{29}{3}.\frac{21}{24}\)
\(=\frac{203}{24}\)
Study well ! >_<
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![](https://rs.olm.vn/images/avt/0.png?1311)
rút gọn thì còn:
\(\frac{179}{176}\)
\(\frac{24.179-24}{24.176+24}\)
\(=\frac{24.\left(179-1\right)}{24.\left(176+1\right)}\)
\(=\frac{24.178}{24.177}=\frac{178}{177}\)