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A = 2012.2016 = (2013 - 1)(2015 + 1)
= 2013.2015 + 2013 - 2015 - 1
= 2013.2015 - 3 < 2013.2015
=> A < B
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a) ta có: \(1-\frac{2012}{2013}=\frac{1}{2013}\)
\(1-\frac{2013}{2014}=\frac{1}{2014}\)
mà \(\frac{1}{2013}>\frac{1}{2014}\) nên \(\frac{2013}{2014}>\frac{2012}{2013}\)
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a.\(10^{30}=10^{3^{10}}=1000^{10}\)
\(2^{100}=2^{10^{10}}=1024^{10}\)
Vì 1024 > 1000 \(\Rightarrow1024^{10}>1000^{10}\Rightarrow10^{30}
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a)Ta có: \(2^{91}=2^{90}x2=\left(2^6\right)^{15}x2=64^{15}x2\)
Vì 6415 >515 =>6415 x 2 >515
Hay 2 91 > 515
b)Ta có: 521=7812514
vì 7812514>2614nên 521>2614
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\(\frac{2013.2015-1}{2010+2013.2014}=\frac{2013.2014+2013-1}{2010+2013.2014}=\frac{2013.2014+2012}{2010+2013.2014}\)
Ta thay: 2013.2014+2012>2010+2013.2014
=>\(\frac{2013.2015-1}{2010+2013.2014}>1\)
\(A=2013.2015