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\(\frac{2011}{2010}\times\frac{2012}{2011}\times\frac{2013}{2012}\times\frac{2014}{2013}\times\frac{1005}{1007}\)
\(=\frac{2014}{2010}\times\frac{1005}{1007}\)
\(=\frac{2\times1007\times1005}{2\times1005\times1007}\)
\(=1\)
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$
2014 x 3 + 4028 x 2 + 2014 x 5 - 2014 x 2
= 2014 x 3 + 2014 x 2 x 2 + 2014 x 5 - 2014 x 2
= 2014 x 3 + 2014 x 4 + 2014 x 5 - 2014 x 2
= 2014 x ( 3 + 4 + 5 - 2 )
= 2014 x 10 = 20140
\(2014\text{×}3+4028\text{×}2+2014\text{×}5-2014\text{×}2\\ =2014\text{×}3+2014\text{×}2\text{×}2+2014\text{×}5-2014\text{×}2\\ =2014\text{×}3+2014\text{×}4+2014\text{×}5-2014\text{×}2\\ =2014\text{×}\left(3+4+5-2\right)=2014\text{×}10=20140\)
= 2011 x 2012 + 2011 x 2 / 2013 x 2014 - 2014 x 2
= 2011 x 2014 / 2014 x 2011 = 1
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