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\(\frac{2}{6}+\frac{2}{12}+...+\frac{2}{x\left(x+1\right):2}=\frac{2009}{2011}\)
\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2009}{2011}\)
\(2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2009}{2011}\)
\(2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2009}{2011}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2009}{2011}:2\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2009}{4022}\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{2009}{4022}\)
\(\frac{1}{x+1}=\frac{1}{2011}\)
=>x+1=2011
=>x=2010
Chào mai xinh đẹp
1<=>( x-4)/2009 -1 +( x-3)/2010-1 -(x-2)/2011-1-(x-1)/2012-1=0
<=> (x-2013)/2009+ (x-2013)/2010-(x-2013)/2011-(x-2013)/2012=0
<=> (x-2013)( 1/2009+1/2010-1/2011-1/2012)=0
=> x-2013=0=> x=2013
pp mai
\(\frac{x-28-124}{2011}+\frac{x-124-2011}{28}+\frac{x-2011-28}{124}\)\(=3\)
\(\Leftrightarrow\frac{x-152}{2011}+\frac{x-2135}{28}+\frac{x-2039}{124}=3\)\(\Leftrightarrow\left(\frac{x-152}{2011}-1\right)+\left(\frac{x-2135}{28}-1\right)+\left(\frac{x-2039}{124}-1\right)=3-1-1-1\)
\(\Leftrightarrow\frac{x-2163}{2011}+\frac{x-2163}{28}+\frac{x-2163}{124}=0\)
\(\Leftrightarrow\left(x-2163\right)\left(\frac{1}{2011}+\frac{1}{28}+\frac{1}{124}\right)=0\)
Vì \(\left(\frac{1}{2011}+\frac{1}{28}+\frac{1}{124}\right)>0\)
\(\Rightarrow x-2163=0\)
\(\Leftrightarrow x=2163\)
Vậy \(x=2163\)
.........................
= \(\frac{1}{2}\). ( \(\frac{2}{1.3}\) + \(\frac{2}{3.5}\) + \(\frac{2}{5.7}\) ... + \(\frac{2}{x.\left(x+2\right)}\) )
= \(\frac{1}{2}\) . ( 1 - \(\frac{1}{3}\) + \(\frac{1}{3}\) - \(\frac{1}{5}\) + \(\frac{1}{5}\) - \(\frac{1}{7}\) + ... + \(\frac{1}{x}\)- \(\frac{1}{x+2}\) )
= ................
Bạn tự làm tiếp nhé ! Chúc bạn học tốt :)
Do \(\left|x+2011\right|\ge0\) với mọi x
\(\left|x+1\right|\ge0\) với mọi x
\(\left|x+2\right|\ge0\) với mọi x
\(\Rightarrow\left|x+2011\right|+\left|x+1\right|+\left|x+2\right|\ge0\) với mọi x\(\Rightarrow4x\ge0\)
\(\Rightarrow x\ge0:4=0\)
Do \(x\ge0\) nên :
\(\left|x+2011\right|=x+2011\)
\(\left|x+1\right|=x+1\)
\(\left|x+2\right|=x+2\)
\(\Rightarrow4x=x+2011+x+2+x+1\)
\(\Rightarrow4x-x-x-x=2011+2+1\)
\(\Rightarrow x=2014\)
điều kiện 4x>=0 => x>=0 vậy tất cả các giá trị tuyệt đối đề dương
nên ta có /x+2011/+/x+1/+/x+2/=4x
<=> x+2011 +x+1+x+2=4x
<=> 4x-x-x-x= 2011+1+2
<=> x= 2014