2/7.8 + 2/8.9 + ....+2/57.58=?
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![](https://rs.olm.vn/images/avt/0.png?1311)
1.2.3...8.9-1.2.3....8-1.2.3...8.8
=1.2.3...8(9-1-8)
=1.2.3...8.0
=0
![](https://rs.olm.vn/images/avt/0.png?1311)
Ai chs opoke đại chiên lh mik nha! Đỏi lấy nick olm hoặc cho mik
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2}{1\cdot2}+\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+........+\frac{2}{8\cdot9}+\frac{2}{9\cdot10}\)
\(=2\cdot\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+......+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\right)\)
\(=2\cdot\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+........+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
\(=2\cdot\left(\frac{1}{1}-\frac{1}{10}\right)\)
\(=2\cdot\frac{9}{10}=\frac{9}{5}\)
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
![](https://rs.olm.vn/images/avt/0.png?1311)
3.(1/4.5+1/5.6+...+1/9.10).x=9/2
3.(1/4-1/5+1/5-1/6+...+1/9-1/10).x=9/2
3.(1/4-1/10).x=9/2
3.3/20.x=9/2
9/20.x=9/2
x=9/2:9/20
x=10
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A = 5.6 + 6.7 + 7.8 + 8.9 +...+ 97.98
=> 3A = 5.6.3 + 6.7.3 + 7.8.3 + 8.9.3 + ...+ 97.98.3
3A = 5.6.(7-4) + 6.7.(8-5) + 7.8(9-6) + 8.9.(10-7) +...+ 97.98.(99-96)
3A = 5.6.7 - 4.5.6 + 6.7.8 -5.6.7 + 7.8.9 - 6.7.8 + 8.9.10 - 7.8.9 + ...+ 97.98.99 - 96.97.98
3A = 97.98.99 - 4.5.6
A = 313 658
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2}{7.8}+\frac{2}{8.9}+...+\frac{2}{57.58}=2\left(\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{57.58}\right)\)
\(=2\left(\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{57}-\frac{1}{58}\right)\)
\(=2\left(\frac{1}{7}-\frac{1}{58}\right)=\frac{2.51}{406}=\frac{51}{203}\)