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= 2012 x (1001-1) + 2013 x (999+1)
= 2012 x 1000 + 2013 x 1000
= 1000 x (2012+2013)
= 1000 x 4025 = 4025000
k mk nha
= 2012 x (1001-1) + 2013 x (999+1)
= 2012 x 1000 + 2013 x 1000
= 1000 x (2012+2013)
= 1000 x 4025 = 4025000
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$
Ta có \(\frac{2011}{2012}>\frac{2011}{2012+2013}\)
\(\frac{2012}{2013}>\frac{2012}{2012+2013}\)
\(\Rightarrow\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011+2012}{2012+2013}\)(ĐPCM)
Học tốt
\(\frac{2011.2013+2014}{2012.2012+2013}=\frac{2011.2013+2013+1}{2012.2012+2012+1}=\frac{2013.\left(2011+1\right)+1}{2012.\left(2012+1\right)+1}=\frac{2013.2012+1}{2012.2013+1}=1\)
Vậy \(\frac{2011.2013+2014}{2012.2012+2013}=1\)
(Dấu . là nhân nha bạn)
\(\frac{2012.2011+2012.11+2000}{2013.2011-2011.2012}=\frac{2012.\left(2011+11\right)+2000}{2011.\left(2013-2012\right)}\)
\(=\frac{2012.2022+2000}{2011}\)
\(=\frac{4068264+2000}{2011}\)
\(=\frac{4070264}{2011}\)
\(=2024\)
~~ HỌC TỐT ~~ !! >-<
Ta có : 2012 x 1001 - 2012 + 2013 x 999 + 2013
= 2012 x (1001 - 1) + 2013 x (999 + 1)
= 2012 x 1000 + 2013 x 1000
= 1000 x (2012 + 2013)
= 1000 x 4025
= 4 025 000
=2014012-2012+2010987+2013
=2012000+2010987+2013
=4025000