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TN
14 tháng 5 2016
\(\frac{2}{6}+\frac{2}{12}+...+\frac{2}{x\left(x+1\right):2}=\frac{2009}{2011}\)
\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2009}{2011}\)
\(2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2009}{2011}\)
\(2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2009}{2011}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2009}{2011}:2\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2009}{4022}\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{2009}{4022}\)
\(\frac{1}{x+1}=\frac{1}{2011}\)
=>x+1=2011
=>x=2010
25 tháng 6 2017
Đặt \(\left(1+5+5^2+5^3+...+5^{2010}+5^{2011}\right)\) là A
\(\Rightarrow5A=5+5^2+5^3+5^4+...+5^{2011}+5^{2012}\)
\(\Rightarrow5A-A=5+5^2+5^3+5^4+...+5^{2011}+5^{2012}-1-5-5^2-5^3-...-5^{2010}-5^{2011}\)
\(\Rightarrow4A=5^{2012}-1\)
\(\Rightarrow A=\frac{1}{4}\left(5^{2012}-1\right)\)
Thay A vào, ta có:
\(\frac{1}{4}\left(5^{2012}-1\right)\left(x-1\right)=5^{2012}-1\)
\(\frac{1}{4}\left(x-1\right)=1\)
\(x-1=4\)
\(x=3\)
VT
4 tháng 3 2023
\(\dfrac{-1}{4}< \dfrac{x}{24}< \dfrac{-1}{6}\\ \dfrac{-6}{24}< \dfrac{x}{24}< \dfrac{-4}{24}\\ \Rightarrow x=-5\)
19 tháng 4 2018
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CC
1
14 tháng 11 2016
2x-2016=2018
2x =2018+2016
2x =4034
x =4034:2
x =2017
3x +1=82
3x =82-1
3x =81
3x =34
x =4
20x-11=20x+2x-12
20x-11=x(20+2)-12
20x-11=22x-12
20x =22x-12+11
20x =22x-1
22x-2x=22x-1
2x =1
x =1:2
x =0,5
(x+1)+(x+2)+(x+3)+(x+4)=26
x+x+x+x+1+2+3+4 =26
4x+10 =26
4x =26-10
4x =16
x =16:4
x =4
NV
24 tháng 6 2016
Ta có: \(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}=\frac{x+4}{2011}+\frac{x+5}{2010}+\frac{x+6}{2009}\)
\(\Rightarrow\frac{x+1}{2014}+1+\frac{x+2}{2013}+1+\frac{x+3}{2012}+1=\frac{x+4}{2011}+1+\frac{x+5}{2010}+1+\frac{x+6}{2009}+1\)
\(\Rightarrow\frac{2015+x}{2014}+\frac{2015+x}{2013}+\frac{2015+x}{2012}=\frac{2015+x}{2011}+\frac{2015+x}{2010}+\frac{2015+x}{2009}\)
\(\Rightarrow\left(2015+x\right)\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}-\frac{1}{2009}\right)=0\)
=> 2015 + x = 0
=> x = -2015
Đặt A = 1+1/3+1/6+...+2/x.(x+1)
A=1+2/6+2/12+...+2/x.(x+1)
A=1+2.(1/6+1/12+...+1/x.(x+1))
A=1+2.(1/2.3+1/3.4+...+1/x.(x+1))
A= 1+2.(1/2-1/3+1/3-1/4+...+1/x-1/x+1)
A=1+2.(1/2-1/x+1)
suy ra 1+2.(1/2-1/x+1)=1/2018/2010
2.(1/2-1/x+1)=1/2018/2010-1
2.(1/2-1/x+1)=1009/1005
1/2-1/x+1=1009/1005:2
1/2-1/x+1=1009/2010
1/x+1=1/2-1009/2010
1/x+1=-2/1005
-2/-2.(x+1)=-2/1005
-2.(x+1)=1005
x+1=1005:(-2)
x+1=-1005/2
x=-1005/2-1
x=-1007/2