8/10+3/5×1/2 ghi ps rõ ràng
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{5}A=\frac{1+5+5^2+...+5^9}{1+5+5^2+...+5^9}=1\)
\(\frac{1}{3}B=\frac{1+3+3^2+...+3^9}{1+3+3^2+...+3^9}=1\)
Vì \(\frac{1}{5}<\frac{1}{3}\)Nên \(\frac{1}{5}A<\frac{1}{5}B\)
Vậy A<B
ai trả lời cũng sai hết rồi
Tui Gợi ý là A > B
Bây giờ các bạn ghi cách giải đi
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{45}\)
\(a=\frac{1}{1.3}+\frac{1}{2.3}+\frac{1}{2.5}+\frac{1}{3.5}+...+\frac{1}{5.9}\)
\(a=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}\right)\)
\(a=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(a=2\left(\frac{1}{2}-\frac{1}{10}\right)\)
=> \(a=2.\frac{2}{5}\)
=> \(a=\frac{4}{5}\)
\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{45}\)
\(\Rightarrow\frac{1}{2}A=\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}\right)\cdot\frac{1}{2}\)
\(=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)
\(=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)
\(\Rightarrow A=\frac{2}{5}:\frac{1}{2}=\frac{4}{5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,\dfrac{6}{11}+6+\dfrac{5}{7}=\dfrac{42+462+55}{77}=\dfrac{559}{77}\)
\(b,\dfrac{9}{8}\times\dfrac{3}{12}:\dfrac{5}{9}=\dfrac{9}{8}\times\dfrac{3}{12}\times\dfrac{9}{5}=\dfrac{243}{480}=\dfrac{81}{160}\)
\(c,\dfrac{8}{7}:4+2=\dfrac{8}{7}\times\dfrac{1}{4}+2=\dfrac{8}{28}+2=\dfrac{2}{7}+2=\dfrac{16}{7}\)
\(d,\dfrac{3}{5}+4:\dfrac{6}{4}=\dfrac{3}{5}+4\times\dfrac{4}{6}=\dfrac{3}{5}+\dfrac{8}{3}=\dfrac{49}{15}\)
`=8/10+3/10`
`=11/10`
\(\dfrac{8}{10}+\dfrac{3}{5}\times\dfrac{1}{2}=\dfrac{8}{10}+\dfrac{3}{10}=\dfrac{11}{10}=1,1\)