\(\dfrac{6^2+3\cdot6^2+3^2}{-13}\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(B=\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+\dfrac{2}{3.4.5}+\dfrac{2}{4.5.6}+\dfrac{2}{5.6.7}+\dfrac{2}{6.7.8}\)
\(=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{6.7}-\dfrac{1}{7.8}\)
\(=\dfrac{1}{1.2}-\dfrac{1}{7.8}\)
\(=\dfrac{1}{2}-\dfrac{1}{56}=\dfrac{27}{56}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{6^3+3.6^2+3}{-13}\)
\(=\frac{216+108+27}{-13}\)
\(=\frac{351}{-13}\)
\(=-27\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{6^3+3.6^2.3^3}{-13}\)
\(=\frac{3^3.2^3+3.3^2.2^2.3^3}{-13}\)
\(=\frac{3^3.2^2.\left(2+3^3\right)}{-13}\)
\(=\frac{3^3.2^2.54}{-13}\)
\(=>....\)
\(\frac{6^3+3\cdot6^2\cdot3^3}{-13}\)
\(=\frac{216+3\cdot36\cdot27}{-13}\)
\(=\frac{216+2916}{-13}\)
\(=\frac{3132}{-13}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, A= \(5\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\right)\)
\(A=5\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\)
\(A=5\left(1-\dfrac{1}{100}\right)\)
\(A=5.\dfrac{99}{100}=\dfrac{99}{20}.\)
b, \(C=1.2.3+2.3.4+...+8.9.10\)
\(4C=1.2.3.4+2.3.4.\left(5-1\right)+...+8.9.10.\left(11-7\right)\)\(4C=1.2.3.4+2.3.4.5-1.2.3.4+...+8.9.10.11-7.8.9.10\)\(4C=8.9.10.11\)
\(C=\dfrac{8.9.10.11}{4}=1980.\)
c, https://hoc24.vn/hoi-dap/question/384591.html
Câu này bạn vào đây mình đã giải câu tương tự nhé.
\(1)A=\dfrac{5}{1.2}+\dfrac{5}{2.3}+...+\dfrac{5}{99.100}\)
\(\Leftrightarrow A=5\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\)
\(\Leftrightarrow A=5\left(1-\dfrac{1}{100}\right)\)
\(\Leftrightarrow A=5\cdot\dfrac{99}{100}\)
\(\Leftrightarrow A=\dfrac{99}{20}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{6^3+3.6^2+3^2}{-13}\)
\(=\frac{\left(2.3\right)^3+3.\left(2.3\right)^2+3^2}{-13}\)
\(=\frac{2^3.3^3+\left(3.3^2\right).2+3^2}{-13}\)
\(=\frac{3^2.\left(2^3.3+3.2+1\right)}{-13}\)
\(=\frac{3^2.31}{-13}\)
\(=\frac{9.31}{-13}\)
\(=\frac{273}{-13}\)
\(=-21\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{6^3+3\cdot6^2+3^3}{-13}\)
\(=\frac{6^2\cdot\left(6+3\right)+3^3}{-13}\)
\(=\frac{6^2\cdot3^2+3^3}{-13}\)
\(=\frac{3^3\cdot\left(6^2+3\right)}{-13}\)
\(=\frac{3^3\cdot39}{-13}\)
\(=-3^3=-27\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1. \(A=\dfrac{2\left(\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{1}{9}-\dfrac{1}{11}\right)}{4\left(\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{1}{9}-\dfrac{1}{11}\right)}=\dfrac{2}{4}=\dfrac{1}{2}\)
2. \(B=\dfrac{1^2.2^2.3^2.4^2}{1.2^2.3^2.4^2.5}=\dfrac{1}{5}\)
3.\(C=\dfrac{2^2.3^2.\text{4^2.5^2}.5^2}{1.2^2.3^2.4^2.5.6^2}=\dfrac{125}{36}\)
4.D=\(D=\left(\dfrac{4}{5}-\dfrac{1}{6}\right).\dfrac{4}{9}.\dfrac{1}{16}=\dfrac{19}{30}.\dfrac{1}{36}=\dfrac{19}{1080}\)
\(=\dfrac{3^2\left(2^2+2^3+1\right)}{-13}=\dfrac{-13\cdot3^2}{13}=-9\)