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Ta có \(A=2015^{2001}=2015.2015^{2000}\)
\(B=2014^{2000}+2014^{2001}=2014^{2000}.\left(1+2014\right)\)\(=2015.2014^{2000}\)
Ta thấy \(2014^{2000}< 2015^{2000}\Rightarrow2015.2014^{2000}< 2015.2015^{2000}\)
\(\Rightarrow2015^{2001}>2014^{2000}+2014^{2001}\)
Vậy A>B
\(2015^{2001}=2015^{2000}.2015;2014^{2000}+2014^{2001}=2014^{2000}.\left(2014+1\right)=2014.2015\)
Ta thấy 20152000.2015 > 20142000.2014
có:A=2000^2001+1/2000^2002+1
=)2000A=2000^2002+2000/2000^2002+1=2000^2002+1+1999/2000^2002+1
=1999/2000^2002+1
lại có:B=2000^2000+1/2000^2001+1
=)2000B=2000^2001+2000/2000^2001+1=2000^2001+1+1999/2000^2001+1
=1999/2000^2001+1
vì 1999/2000^2002+1 < 1999/2000^2001+1
=)2000A < 2000B hay A<B
Ta có : A = 20002016 + 20002017
= 20002016.(1 + 2000)
= 20002016.2001
< 20012016.2001
= 20012017 = B
=> A < B
Vậy A < B
B=20002017+2017 ,A=20002016+20002017
Mà 20002016>2017
=>A>B
ta có :
\(10A=\frac{10^{2014}+10}{10^{2014}+1}=\frac{\left(10^{2014}+1\right)+9}{10^{2014}+1}=1+\frac{9}{10^{2014}+1}\)
\(10B=\frac{10^{2015}+10}{10^{2015}+1}=\frac{\left(10^{2015}+1\right)+9}{10^{2015}+1}=1+\frac{9}{10^{2015}+1}\)
ta thấy \(10^{2014}+1< 10^{2015}+1\Rightarrow\frac{9}{10^{2014}+1}>\frac{9}{10^{2015}+1}\Rightarrow10A>10B\Rightarrow A>B\)
\(A=2015^{2001}=2015^{2000}.2015\)
\(B=2014^{2000}+2014^{2001}=2014^{2000}.\left(2014+1\right)=2014.2015\)
Ta thấy \(2015^{2000}.2015>2014^{2000}.2015\)
\(\Rightarrow A>B\)