2011 nhân 2012 + 4022
phần
2013 nhân 2014 - 4028
tính nhanh
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\(\frac{2011}{2010}\times\frac{2012}{2011}\times\frac{2013}{2012}\times\frac{2014}{2013}\times\frac{1005}{1007}\)
\(=\frac{2014}{2010}\times\frac{1005}{1007}\)
\(=\frac{2\times1007\times1005}{2\times1005\times1007}\)
\(=1\)
= 2011 x 2012 + 2011 x 2 / 2013 x 2014 - 2014 x 2
= 2011 x 2014 / 2014 x 2011 = 1
k mk nha
a,ta có:
A=2011^2012-2011^2011
=2011^2011(2011-1)
=2011^2011.2010
và B = 2011^2013-2011^2012
=2011^2012(2011-1)
=2011^2012.2010
Vì 2011^2011<2011^2012 => 2011^2011.2010< 2011^2012.2010
=>A<B
a,ta có:
A=2011^2012-2011^2011
=2011^2011(2011-1)
=2011^2011.2010
và B = 2011^2013-2011^2012
=2011^2012(2011-1)
=2011^2012.2010
Vì 2011^2011<2011^2012 => 2011^2011.2010< 2011^2012.2010
=>A<B
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$
\(a,\left(1-\dfrac{1}{10}\right)\times\left(1-\dfrac{1}{11}\right)\times\left(1-\dfrac{1}{12}\right)\times\left(1-\dfrac{1}{13}\right)\times\left(1-\dfrac{1}{14}\right)\times\left(1-\dfrac{1}{15}\right)=\dfrac{9}{10}\times\dfrac{10}{11}\times\dfrac{11}{12}\times\dfrac{12}{13}\times\dfrac{13}{14}\times\dfrac{14}{15}=\dfrac{9}{15}=\dfrac{3}{5}\)
\(b,\dfrac{2013\times2012-2}{2011+2011\times2013}=\dfrac{\left(2014-1\right)\times2012-2}{2011\times\left(2013+1\right)}=\dfrac{2014\times2012-2012-2}{2011\times2014}=\dfrac{2014\times2012-2014}{2011\times2014}=\dfrac{2014\times\left(2012-1\right)}{2011\times2014}=\dfrac{2011\times2014}{2011\times2014}=1\)
(2011 × 2012 + 4022) /(2013 × 2014 - 4028)= 0
(2011 × 2012 + 4022) /(2013 × 2014 - 4028)=1