2/4.5+2/5.6+ ........ 2/65.66
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\(\frac{2}{1\cdot2}+\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+........+\frac{2}{8\cdot9}+\frac{2}{9\cdot10}\)
\(=2\cdot\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+......+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\right)\)
\(=2\cdot\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+........+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(=2\cdot\left(\frac{1}{1}-\frac{1}{10}\right)\)
\(=2\cdot\frac{9}{10}=\frac{9}{5}\)
đúng nha !
Ta có:
2/1.2+2/2.3+2/3.4+2/4.5+2/5.6+2/6.7+2/7.8+2/8.9+2/9.10
=2.(1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9+1/9.10)
=2.(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)
=2.(1-1/10)
=2.9/10
=9/5
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phân số thứ nhất =16/11
phân số thứ hai = -5/9
phân số thứ ba = 10/77
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\(\frac{\sqrt{2^3\cdot3^4\cdot5^5\cdot6^6\cdot7^7}}{2^2\cdot3^2\cdot5^6\cdot6^3\cdot7^3}=\frac{2\cdot3^2\cdot5^2\cdot6^3\cdot7^3\cdot\sqrt{2\cdot5\cdot7}}{2^2\cdot3^2\cdot5^6\cdot6^3\cdot7^3}=\frac{\sqrt{2\cdot5\cdot7}}{2\cdot5^4}=\frac{\sqrt{70}}{1250}\)
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a: \(\dfrac{4\cdot5+4\cdot11}{8\cdot7+4\cdot3}=\dfrac{4\cdot16}{4\left(2\cdot7+3\right)}=\dfrac{16}{17}=\dfrac{11088}{11781}\)
\(\dfrac{-15\cdot8+10\cdot7}{5\cdot6+20\cdot3}=\dfrac{-120+170}{30+60}=\dfrac{50}{90}=\dfrac{5}{9}=\dfrac{6545}{11781}\)
\(\dfrac{2^4\cdot5^2\cdot7}{2^3\cdot5\cdot7^2\cdot11}=2\cdot5\cdot\dfrac{1}{77}=\dfrac{10}{77}=\dfrac{1530}{11781}\)
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\(\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{65.66}\)
\(=2\left(\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{65.66}\right)\)
\(=2\left(\frac{5-4}{4.5}+\frac{6-5}{5.6}+...+\frac{66-65}{65.66}\right)\)
\(=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{65}-\frac{1}{66}\right)\)
\(=2\left(\frac{1}{4}-\frac{1}{66}\right)\)
\(=\frac{31}{66}\)