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a = 2014100 - 201499 = 201499(2014 - 1) = 201499.2013
b = 201499 - 201498 = 201498(2014 - 1) = 201498.2013
Vì 201499.2013 > 201498.2013 => a > b
A= 2014^100 - 2014^99 = 2014^99 ( 2014 -1) = 2014^99 . 2013
B = 2014^99 - 2014^98 = 2014^98 ( 2014 - 1) = 2013.2014^98
Vì 2014^98 <2014^99 > 2013.2014^98 < 2013.2014^99
=> B < A
cùng nhân tử với 2014>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
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
a,A=2^0+2^1+2^2+...+2^2014
2A=2^1+2^2+2^3+...+2^2015
2A-A=(2^1+2^2+2^3+...+2^2015)-(2^0+2^1+2^2+...+2^2014)
A=2^2015-2^0=2^2015-1=B
=>A=B
b,A=2014.2016=2014.(2015+1)=2014.2015+2014
B=2015^2=2015.2015=(2014+1).2015=2014.2015+2015
Vì 2014<2015 => 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 \(2015^{2000}.2015>2014^{2000}.2015\)
\(\Rightarrow A>B\)
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