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\(Q=\frac{2010+2011+2012}{2011+2012+2013}\)
\(Q=\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
Ta có :
\(\hept{\begin{cases}\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\\\frac{2011}{2012}>\frac{2011}{2011+2012+2013}\\\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\end{cases}}\)
\(\Rightarrow P>Q\)
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Ta có:
2^16 = 2^13 x 2^3
= 2^13 x 8
=> 7. 2^13 < 2 ^13 . 8
=> Vậy 7. 2^13 < 2 ^13 . 8
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2A = 2( 1 + 2 + 22 + .... + 22010 )
= 2 + 22 + 23 + .... + 22011
2A - A = ( 2 + 22 + 23 + .... + 22011) - ( 1 + 2 + 22 + .... + 22010 )
A = 22011 - 1 > 22010 - 1 = B
=> A > B
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\(2^{16}=2^{13}.2^3=2^{13}.8\)
Mà \(8>7\Rightarrow7.2^{13}< 2^{16}\)
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a) 32012 = (32)1006 = 91006 ; 23018 = (23)1006 = 81006
Vì 9 > 8 nên 91006 > 81006 => 32012 > 23018
b) Có 1 < 25 = 32 nên 52010 < 25.52010
7.22010 > 22014