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2014/2014.2015=1/2015
2015/2015.2016=1/2016
vì 1/2015>1/2016=>2014/2014.2015>2015/2015.2016
\(\frac{2014}{2014\cdot2015}=\frac{1}{1\cdot2015}=\frac{1}{2015}\)
\(\frac{2015}{2015\cdot2016}=\frac{1}{1\cdot2016}=\frac{1}{2016}\)
Mà \(\frac{1}{2015}>\frac{1}{2016}\)
\(=>\frac{2014}{2014\cdot2015}>\frac{2015}{2015\cdot2016}\)
Ta có \(\frac{2014}{2014\cdot2015}\)=\(\frac{2014:2014}{2014\cdot2015:2014}\)=\(\frac{1}{2015}\)
\(\frac{2015}{2015\cdot2016}\)=\(\frac{2015:2015}{2015\cdot2016:2015}\)=\(\frac{1}{2016}\)
Vì \(\frac{1}{2015}\)>\(\frac{1}{2016}\)=>\(\frac{2014}{2014\cdot2015}\)>\(\frac{2015}{2015\cdot2016}\)
a) A=20142=2014.2014<2014.2015=B
=>A<B
b) A=20142=2014.2014=(2010+4).2014=2010.2014+4.2014
B=2010.2018=2010.(2014+4)=2010.2014+4.2010
Vì 2014>2010
=>4.2014>4.2010
=>2010.2014+4.2014>2010.2014+4.2010
=>A>B
c) A=20143=2014.2014.2014<2014.2015.2014<2014.2015.2016=B
=>A<B
A=-2015/2015x2016
A=-1/2016
B=-2014/2014x2015
B=-1/2015
vi 2016>2015,-1/2016>-1/2015
vay A>B
b) Ta có: \(A=\dfrac{10^{2009}+1}{10^{2010}+1}\)
\(\Leftrightarrow10A=\dfrac{10^{2010}+10}{10^{2010}+1}=1+\dfrac{9}{10^{2010}+1}\)
Ta có: \(B=\dfrac{10^{2010}+1}{10^{2011}+1}\)
\(\Leftrightarrow10B=\dfrac{10^{2011}+10}{10^{2011}+1}=1+\dfrac{9}{10^{2011}+1}\)
Ta có: \(10^{2010}+1< 10^{2011}+1\)
\(\Leftrightarrow\dfrac{9}{10^{2010}+1}>\dfrac{9}{10^{2011}+1}\)
\(\Leftrightarrow\dfrac{9}{10^{2010}+1}+1>\dfrac{9}{10^{2011}+1}+1\)
\(\Leftrightarrow10A>10B\)
hay A>B
Ta có : \(A\text{=}\dfrac{2013.2014-1}{2013.2014}\text{=}\dfrac{2013.2014}{2013.2014}-\dfrac{1}{2013.2014}\text{=}1-\dfrac{1}{2013.2014}\)
\(B\text{=}\dfrac{2014.2015-1}{2014.2015}\text{=}\dfrac{2014.2015}{2014.2015}-\dfrac{1}{2014.2015}\text{=}1-\dfrac{1}{2014.2015}\)
\(Ta\) có : \(\dfrac{1}{2013.2014}>\dfrac{1}{2014.2015}\)
\(\Rightarrow A< B\)
a) Ta có:
a = 1002.1001
a = 1002.( 1000 + 1 )
a = 1002.1000 + 1002
b = 1003.1000
b = ( 1002 + 1 ).1000
b = 1002.1000 + 1000
Vậy a = 1002.1000 + 1002
b = 1002.1000 + 1000
=> a > b
b) Ta có:
a = 2002.2002
a = 2002. ( 2000 + 2 )
a = 2002.2000 + 2002.2
a = 2002.2000 + 4004
b = 2000.2004
b = 2000. ( 2002 + 2 )
b = 2000.2002 + 2000.2
b = 2000.2002 + 4000
Vậy a = 2002.2000 + 4004
b = 2000.2002 + 4000
=> a > b
c) Ta có:
a = 2016.2016
a = 2016.( 2014 + 2 )
a = 2016.2014 + 2016.2
b = 2014.2015
b = 2014. ( 2016 - 1 )
b = 2014.2016 - 2014
Vậy a = 2016.2014 + 2016.2
b = 2014.2016 - 2014
=> a > b
