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a) 5x - x = 64 \(\Rightarrow\) 4x = 64 \(\Rightarrow\) x = 16
b) \(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{9\cdot10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}\)
\(=\frac{9}{10}\)
c) \(B=\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+...+\frac{2}{99\cdot101}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\)
\(=1-\frac{1}{101}\)
\(=\frac{100}{101}\)
d) \(C=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+...+\frac{1}{97\cdot99}\)
\(=\frac{1}{2}\cdot\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+...+\frac{2}{97\cdot99}\right)\)
\(=\frac{1}{2}\cdot\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+..+\frac{1}{97}-\frac{1}{99}\right)\)
\(=\frac{1}{2}\cdot\left(1-\frac{1}{99}\right)\)
\(=\frac{1}{2}\cdot\frac{98}{99}\)
\(=\frac{49}{99}\)
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a) bạn xem lại đề nha
b)
\(B=\dfrac{1}{1.3}\)\(+\dfrac{1}{3.5}+...+\dfrac{1}{2003.2005}\)
\(B=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2003}-\dfrac{1}{2005}\right)\)
\(B=\dfrac{1}{2}\left(1-\dfrac{1}{2005}\right)=\dfrac{1002}{2005}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
S=(1/1.3+1/3.5+.....+1/7.9)+(1/2.4+1/4.8+1/8.10)
2S=1/2.(1-1/3+1/5-1/5+....+1/7-1/9)+(1/2-1/4+1/4-1/8+1/8-1/10)
2S=1/2.(1-1/9)+(1/2-1/10)
2S=1/2.(8/9+2/5)
![](https://rs.olm.vn/images/avt/0.png?1311)
S =\(\frac{1}{2}\left(1-\frac{1}{3}\right)+\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}\right)+....\frac{1}{2}\left(\frac{1}{8}-\frac{1}{10}\right)\)
S = 1/2 ( 1 -1/3 +1/2-1/4+......+ 1/8-1/10)
S = 1/2(1+1/2-1/9-1/10)
S= 29/45
Bạn nói cô giáo sửa đề thành:
Tính tổng S=1/1.3+1/2.4+1/3.5+.....+1/\(7\).9+1/8.10
chứ không tổng S lẻ lắm, chẳng ai muốn tính cả.
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+...+\frac{1}{2001\times2003}+\frac{1}{2003\times2005}=\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{2001\times2003}+\frac{2}{2003\times2005}\right)\)
\(=\frac{1}{2}\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2001}-\frac{1}{2003}+\frac{1}{2003}-\frac{1}{2005}\right)=\frac{1}{2}\times\left(1-\frac{1}{2005}\right)=\frac{1}{2}\times\frac{2004}{2005}=\frac{1002}{2005}\)
Chúc bạn học tốt
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Cố gắng lên (tự nhủ)
\(S=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2017.2019}\)
\(2S=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\)
\(2S=1-\frac{1}{2019}=\frac{2018}{2019}\)
\(S=\frac{1009}{2019}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{4}{1.3}.\dfrac{9}{2.4}.\dfrac{16}{3.5}.....\dfrac{100}{9.10}\)
\(=\dfrac{2.2}{1.3}.\dfrac{3.3}{2.4}.\dfrac{4.4}{3.5}.....\dfrac{10.10}{9.10}\)
\(=\dfrac{2.3.4.....10}{1.2.3......9}.\dfrac{2.3.4.....10}{3.4.5.....10}\)
\(=10.2\)
\(=20\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2017.2019}\)
\(=1-\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+..+\frac{1}{2017}-\frac{1}{2019}\div2\)
\(=\left(1-\frac{1}{2019}\right)\div2\)
\(=\frac{2018}{2019}\div2\)
\(=\frac{1009}{2019}\)
Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2017.2019}\)
\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2017.2019}\)
\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\)
\(2A=1-\frac{1}{2017}\)
\(2A=\frac{2016}{2017}\)
\(A=\frac{2016}{2017}:2\)
\(A=\frac{1008}{2017}\)
=1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9)+1/9.10
=1/2(1-1/9)+1/90
=1/2.8/9+1/90=4/9+1/90=41/90