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AH
Akai Haruma
Giáo viên
13 tháng 9

Lời giải:

\(x=\frac{1}{2^{2009}}+\frac{2}{2^{2008}}+\frac{3}{2^{2007}}+....+\frac{2008}{2^2}+\frac{2009}{2}\)

\(2x = \frac{1}{2^{2008}}+\frac{2}{2^{2007}}+\frac{3}{2^{2006}}+...+\frac{2008}{2}+2009\)

\(\Rightarrow x=2x-x=2009-\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^{2008}}-\frac{1}{2^{2009}}\)

\(\Rightarrow 2009-x=\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2008}}+\frac{1}{2^{2009}}\)

\(\Rightarrow 2(2009-x)=1+\frac{1}{2}+....+\frac{1}{2^{2007}}+\frac{1}{2^{2008}}\)

\(\Rightarrow 2(2009-x)-(2009-x)=1-\frac{1}{2^{2009}}\)

\(\Rightarrow 2009-x=1-\frac{1}{2^{2009}}\\ \Rightarrow x=2009-(1-\frac{1}{2^{2009}})=2008+\frac{1}{2^{2009}}\)

 

a)=> (2008+x).2008/2=2008

=>(2008+x)=2

=>x=-2006

3 tháng 1 2021

\(\frac{x-1}{2009}+\frac{x-2}{2008}=\frac{x-3}{2007}+\frac{x-4}{2006}\)

\(\Leftrightarrow\frac{x-1}{2009}-1+\frac{x-2}{2008}-1=\frac{x-3}{2007}-1+\frac{x-4}{2006}-1\)

\(\Leftrightarrow\frac{x-2010}{2009}+\frac{x-2010}{2008}-\frac{x-2010}{2007}-\frac{x-2010}{2006}=0\)

\(\Leftrightarrow\left(x-2010\right)\left(\frac{1}{2009}+\frac{1}{2008}-\frac{1}{2007}-\frac{1}{2006}\ne0\right)=0\)

\(\Leftrightarrow x=2010\)

11 tháng 2 2017

\(\Leftrightarrow\left(\frac{x-1}{2009}-1\right)+\left(\frac{x-2}{2008}-1\right)=\left(\frac{x-3}{2007}-1\right)+\left(\frac{x-4}{2006}-1\right)\)

\(\Leftrightarrow\frac{x-2010}{2009}+\frac{x-2010}{2008}=\frac{x-2010}{2007}+\frac{x-2010}{2006}\)

\(\Leftrightarrow\frac{x-2010}{2009}+\frac{x-2010}{2008}-\frac{x-2010}{2007}-\frac{x-2010}{2006}=0\)

\(\Leftrightarrow\left(x-2010\right)\left(\frac{1}{2009}+\frac{1}{2008}+\frac{1}{2007}+\frac{1}{2006}\right)=0\)

\(\Rightarrow x-2010=0\Rightarrow x=2010\)

15 tháng 9 2021

Tag thầy Lâm không :)???

1 tháng 8 2015

(x-4)/2007 + (x-3)/2008)= (x-2)/2009 + (x-1)/2010 
=[(x-4)/2007 -1]+[(x-3)/2008 -1]=[(x-2)/2009 -1]+[(x-1)/2010 -1] 
=(x-2011)/2007+(x-2011)/2008=(x-2011)/... 
=(x-2011)(1/2007+1/2008-1/2009-1/2010)... 
suy ra x=2010 

11 tháng 4 2016

\(\dfrac{x}{2008}+\dfrac{x}{2009}-\dfrac{x}{2007}=1+\dfrac{1}{2008}-\dfrac{1}{2009}-\dfrac{2}{2007}\)

\(\Rightarrow x = \dfrac{2007.2008.2009+2009.2007-2008.2007-2.2008.2009}{2009.2007+2008.2007-2008.2009}\)

11 tháng 4 2016

sai rồi banhqua

 

7 tháng 11 2017

2010 nha

25 tháng 9 2016

\(\Rightarrow\left(\frac{x+1}{2009}+1\right)+\left(\frac{x+2}{2008}+1\right)=\left(\frac{x+3}{2007}+1\right)+\left(\frac{x+4}{2006}+1\right)\)

\(\Rightarrow\left(\frac{x+1}{2009}+\frac{2009}{2009}\right)+\left(\frac{x+2}{2008}+\frac{2008}{2008}\right)=\left(\frac{x+3}{2007}+\frac{2007}{2007}\right)+\left(\frac{x+4}{2006}\frac{2006}{2006}\right)\)

\(\Rightarrow\frac{x+2010}{2009}+\frac{x+2010}{2008}=\frac{x+2010}{2007}+\frac{x+2010}{2006}\)

\(\Rightarrow\frac{x+2010}{2009}+\frac{x+2010}{2008}-\frac{x+2010}{2007}-\frac{x+2010}{2006}=0\)

\(\Rightarrow\left(x+2010\right)\left(\frac{1}{2009}+\frac{1}{2008}-\frac{1}{2007}-\frac{1}{2006}\right)=0\)

Vì \(\frac{1}{2009}+\frac{1}{2008}-\frac{1}{2007}-\frac{1}{2006}\ne0\)

=>x+2010=0

=>x=-2010

Vậy x = -2010