2 + 5 + 8 + ... + 101
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
B=1+2-(3+4)+5+6-..-100+101
B=(3+11+19+...+195)-(7+15+...+199)+101
B=25.99-25.103+101
B=-100+101=1
Vậy B=1
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{-2}{5}+\left(\dfrac{4}{6}-\dfrac{1}{15}\right)-\dfrac{-1}{10}\\ =\dfrac{-2}{5}+\dfrac{3}{5}+\dfrac{1}{10}\\ =\dfrac{1}{5}+\dfrac{1}{10}\\ =\dfrac{3}{10}\\ \dfrac{1}{2}-\left(\dfrac{-7}{3}+\dfrac{2}{5}\right)+\dfrac{1}{8}\\ =\dfrac{1}{2}+\dfrac{29}{15}+\dfrac{1}{8}\\ =\dfrac{73}{30}\\ =\dfrac{73}{30}+\dfrac{1}{8}\\ =\dfrac{307}{120}\)
\(-\dfrac{2}{5}+\left(\dfrac{4}{6}-\dfrac{1}{15}\right)-\left(-\dfrac{1}{10}\right)\)
\(=-\dfrac{2}{5}+\dfrac{3}{5}+\dfrac{1}{10}\)
\(=\dfrac{1}{5}+\dfrac{1}{10}\)
\(=\dfrac{2}{10}+\dfrac{1}{10}=\dfrac{3}{10}\)
\(\dfrac{1}{2}-\left(-\dfrac{7}{3}+\dfrac{2}{5}\right)+\dfrac{1}{8}\)
\(=\dfrac{1}{2}+\dfrac{29}{15}+\dfrac{1}{8}\)
\(=\dfrac{73}{30}+\dfrac{1}{8}=\dfrac{307}{120}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài làm
\(M=\frac{3^2}{2.5}+\frac{3^2}{5.8}+\frac{3^2}{8.11}+...+\frac{3^2}{98.101}\)
\(M=3^2\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{98}-\frac{1}{101}\right)\)
\(M=9\left(\frac{1}{2}-\frac{1}{101}\right)\)
\(M=9.\frac{101-2}{202}\)
\(M=9.\frac{99}{202}\)
\(M=\frac{891}{202}\)
Vậy \(M=\frac{891}{202}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(M=3\left(\frac{3}{2x5}+\frac{3}{5x8}+\frac{3}{8x11}+...+\frac{3}{98.101}\right).\)
\(M=3\left(\frac{5-2}{2.5}+\frac{8-5}{5.8}+\frac{11-8}{8.11}+...+\frac{101-98}{98.101}\right)\)
\(M=3\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{98}-\frac{1}{101}\right)=3\left(\frac{1}{2}-\frac{1}{101}\right)=\frac{3.99}{202}\)