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B=1/1.2.3 +1/2.3.4 +1/3.4.5 +.....+1/9.10.11
=1/2.(2/1.2.3 +2/2.3.4 +2/3.4.5 +.......+2/9.10.11)
=1/2.(1/1.2 -1/2.3 +1/2.3 -1/3.4 +1/4.5 +........+1/9.10 -1/10 .11)
=1/2 .(1/1.2 -1/10.11)
= 1/2 .27/55
=27/110
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu a đề không chính xác
câub) B= \(\frac{1}{1.2.3}\frac{ }{ }\)+\(\frac{1}{2.3.4}\)+\(\frac{1}{3.4.5}\)+......+\(\frac{1}{9.10.11}\)
B= \(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}\right)\)+.........+ \(\frac{1}{2}\left(\frac{1}{9.10}-\frac{1}{10.11}\right)\)
B= \(\frac{1}{2}\left(\frac{1}{2}-\frac{1}{10.11}\right)\)= \(\frac{27}{55}\)
B=1/1.2.3 +1/2.3.4 +1/3.4.5 +.....+1/9.10.11
=1/2.(2/1.2.3 +2/2.3.4 +2/3.4.5 +.......+2/9.10.11)
=1/2.(1/1.2 -1/2.3 +1/2.3 -1/3.4 +1/4.5 +........+1/9.10 -1/10 .11)
=1/2 .(1/1.2 -1/10.11)
= 1/2 .27/55
=27/110
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:\(B=\dfrac{1}{6}+\dfrac{1}{24}+\dfrac{1}{60}+...+\dfrac{1}{990}\)
\(2B=\dfrac{2}{6}+\dfrac{2}{24}+\dfrac{2}{60}+...+\dfrac{2}{990}\)
\(2B=\dfrac{2}{1\cdot2\cdot3}+\dfrac{2}{2\cdot3\cdot4}+\dfrac{2}{3\cdot4\cdot5}+...+\dfrac{2}{9\cdot10\cdot11}\)
\(2B=\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}+\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+\dfrac{1}{3\cdot4}-\dfrac{1}{4\cdot5}+...+\dfrac{1}{9\cdot10}-\dfrac{1}{10\cdot11}\)
\(2B=\dfrac{1}{1\cdot2}-\dfrac{1}{10\cdot11}\)
\(2B=\dfrac{27}{55}\)
\(B=\dfrac{27}{55}:2\)
\(B=\dfrac{27}{110}\)
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