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\(\dfrac{2}{2\cdot3}+\dfrac{2}{3\cdot4}+\dfrac{2}{4\cdot5}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2008}{2010}\\ 2\cdot\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{2008}{2010}\\ \dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2008}{2010}:2\\ \dfrac{1}{2}-\dfrac{1}{x+1}=\dfrac{1004}{2010}\\ \dfrac{1}{x+1}=\dfrac{1}{2}-\dfrac{1004}{2010}\\ \dfrac{1}{x+1}=\dfrac{1}{2010}\\ \Rightarrow x+1=2010\\ \Rightarrow x=2009\)
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a.|x-1|=3
=>x-1=3 hoặc x-1=-3
=>x=4 hoăc x=-2
vậy...
b.2x+17=15
=>2x=15-17
=>2x=-2
=>x=-1
vậy...
c.tự giải
d.4x-15=-75-x
=>4x+x=-75+15
=>5x=-60
=>x=-12
vậy...
2.2+(-3)+4+...+(-2011)+2012
=(-3+2)+...+(-2011+2010)+2012 (có 2010 cặp)
=-1.2010+2012
=-2010+2012=2
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`Answer:`
`1/3+1/6+1/10+...+2/(x.(x+1))=2008/2010`
`=2/6+2/12+2/20+...+2/(x.(x+1))=2008/2010`
`=2/(2.3)+2/(3.4)+2/(4.5)+...+(2)/(x.(x+1))=2008/2010`
`=2.(1/2-1/3+1/3-1/4+...+1/x(x+1))=2008/2010`
`=1/2-1/3+1/3-1/4+...+1/x-1/(x+1)=1004/2010`
`=1/2-1/(x+1)=1004/2010`
`=>1/(x+1)=1/2-1004/2010`
`=>1/(x+1)=1/2010`
`=>x+1=2010`
`=>x=2010-1`
`=>x=2009`
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\(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{x.\left(x+1\right)}=\frac{2008}{2010}.\)
\(2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2008}{2010}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{502}{1005}\)
\(\frac{1}{x+1}=\frac{1}{2010}\)
=> x + 1 = 2010
=> x = 2009
Ta có : \(\frac{2}{2\times3}+\frac{2}{3\times4}+....+\frac{2}{x\times\left(x+1\right)}=\frac{2008}{2010}\)
\(\Rightarrow2\times\left(\frac{1}{2\times3}+.....+\frac{1}{x\times\left(x+1\right)}\right)=\frac{1004}{1005}\)
\(\Rightarrow2\times\left(\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{1004}{1005}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{1004}{1005}:2\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{502}{1005}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{502}{1005}=\frac{1}{2010}\)
\(\Rightarrow x+1=2010\)
\(\Rightarrow x=2010-1=2009\)
Câu hỏi của Edogawa Conan - Toán lớp 6 | Học trực tuyến
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