Tìm x biết 1/3+1/6+1/10+2/x.(x+1)=2010/1006
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LD
18 tháng 7 2017
\(3.\)
\(\frac{x-1}{2011}+\frac{x-2}{2010}+\frac{x-3}{2009}=\frac{x-4}{2008}\)
\(\Rightarrow\)\(\frac{x-1}{2011}-1+\frac{x-2}{2010}-1+\frac{x-3}{2009}-1-\frac{x-4}{2008}+1+2=0\)
\(\Rightarrow\)\(\frac{x-1}{2011}-\frac{2011}{2011}+\frac{x-2}{2010}-\frac{2010}{2010}+\frac{x-3}{2009}-\frac{2009}{2009}-\frac{x-4}{2008}+\frac{2008}{2008}=0\)
\(\Rightarrow\)\(\frac{x-2012}{2011}+\frac{x-2012}{2010}+\frac{x-2012}{2009}-\frac{x-2012}{2008}=0\)
\(\Rightarrow\)\(x-2012\left(\frac{1}{2011}+\frac{1}{2010}+\frac{1}{2009}+\frac{1}{2008}\right)=0\)
\(\Rightarrow\)\(x=2012\)
TT
1
YN
7 tháng 4 2022
`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`
NP
3
TT
1
4 tháng 5 2015
Ta có : 1/3+1/6+1/10+ .....+2/x.(x+1)=2010/2012
=>2/6+2/12+2/20+........+2/x(x+1)=2010/2012
=>2.(1/2.3+1/3.4+1/4.5+.....+1/x.(x+1)=2010/2012
................................
Bạn tự làm tiếp nhé ! x=1005
NT
0
S
0
NM
1
13 tháng 8 2015
theo đề bài ta có
1+ 1/3 +1/6+...+2/x(x+1)=1+2009/2010
=>1/3+1/6+....+2/x(x+1)=2009/2010
=>1/2(2+1):2+1/3(3+1):2+.....+1/x(x+1):2=2009/2010
=>2/2(2+1)+2(3+1)+....+2/x(x+1)=2009/2010
=>2(1/2.3+1/3.4+....+1/x(x+1)=2009/2010
=>1/2-1/3+1/3-1/4+.....+1/x-1/x+1=2009/2010:2
=>1/2-1/x+1=2009/4020
=>1/x+1=1/2-2009/4020
=>1/x+1=1/4020
=>x+1=4020
=>x=4020-1
=>x=4019
TN
0
TT
1
1/3+1/6+1/10+2/x.(x+1)=2010/1006
1/6+1/12+1/20+1/x.(x+1)=2010/2012
1/2.3+1/3.4+1/4.5+1/x.(x+1)=1005/1006
1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/x.(x+1)=1005/1006
1/2 - 1/5 + 1/x.(x+1)=1005/1006
3/10+1/x.(x+1)=1005/1006
1/x.(x+1)=1005/1006 - 3/10
1/x.(x+1)=1758/2515
x.(x+1)=1:1758/2515
x.(x+1)=2515/1758
Đến đây thì mình chịu òi!