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$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$
Vì \(2012\times2013< 2012\times2013+1\)và \(2013>2012\)
\(\Rightarrow\)\(\frac{2012\times2013}{2012\times2013+1}< 1< \frac{2013}{2012}\)
\(\Rightarrow\)\(\frac{2012\times2013}{2012\times2013+1}< \frac{2013}{2012}\)
\(\Rightarrow\)\(A< B\)
Vậy \(A< B\)
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ta có : \(\frac{2012\times2013}{2012\times2013}\)có giá trị = 1.nên A có giá trị bằng 2
ta thấy : B = 1,000497018 => A > B
nhớ k nhá
\(\frac{2011.2013+2014}{2012.2012+2013}=\frac{2011.2013+2013+1}{2012.2012+2012+1}=\frac{2013.\left(2011+1\right)+1}{2012.\left(2012+1\right)+1}=\frac{2013.2012+1}{2012.2013+1}=1\)
Vậy \(\frac{2011.2013+2014}{2012.2012+2013}=1\)
(Dấu . là nhân nha bạn)
Đặt phân thức trên là D
=> D=(1+1+1+1+...+1+2013/2+2012/3+...+2/2013+1/2014)/(1/2+1/3+1/4+...+1/2014)
=> D=(1+2013/2+1+2012/3+1+2011/4+...+1+2/2013+1+1/2014+1)/(1/2+1/3+1/4+1/5+...+1/2014)
=> D=(2015/2+2015/3+2015/4+...+2015/2013+2015/2014+1)/(1/2+1/3+1/4+...+1/2014)
=> D=[2015*(1/2+1/3+1/4+1/5+....+1/2014)]/(1/2+1/3+1/4+1/5+...+1/2014)
=> D=2015
\(\frac{2012+2013+2014}{2014\cdot2015+2016}=1\)
\(=1+\dfrac{1}{2012}-1-\dfrac{1}{2013}-\dfrac{1}{2012}+\dfrac{1}{2013}=0\)
= 0