Cho A =1 + 2012+ 20122 + 20123+ 20124+........+ 201271+ 201272 và B= 201273-1.So sánh A và B
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A = 1 + 2012 + 2012^2 + ... + 2012^71 + 2012^72
2012A = 2012 + 2012^2 + 2012^3 + ... + 2012^72 + 2012^73
2012A - A = ( 2012 + 2012^2 + 2012^3 + ... + 2012^72 + 2012^73) - ( 1 + 2012 + 2012^2 + ... + 2012^71 + 2012^72)
2011A = 2012^73 - 1 = B
=> A = 2012^73 - 1/2011
=> A < B
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có A=1+2012+20122+...+201272
A.2012=2012+20122+...+201272+201273
A.2012-A=(2012+20122+...+201272+201273)-(1+2012+20122+...+201272)
A.2011=201273-1
A=(201273-1):2011
Vì 201273-1=201273-1 suy ra A<B
![](https://rs.olm.vn/images/avt/0.png?1311)
A=1+2012+2012 mũ 2 + 2012 mũ 3+.............+2012 mũ 72
A=2012^0+2012^1+2012^2+....+2012^72
2012A=2012^1+2012^2+.....+2012^73
2012A-A=2012^73-1
A=(2012^73-1)/2011<2012^73-1
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(A=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)=\dfrac{1}{2}\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)=\dfrac{1}{2}\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)=\dfrac{1}{2}\left(3^{32}-1\right)< 3^{32}-1=B\)
b) \(A=2011.2013=\left(2012-1\right)\left(2012+1\right)=2012^2-1< 2012^2=B\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=1+2012+20122+20123+.....+201272
=>2012A=2012+20122+20123+20124+...+201273
=>2012A-A=(2012+20122+20123+20124+...+201273)-(1+2012+20122+20123+....+201272)
=>2011A=201273-1
=>\(A=\frac{2012^{73}-1}{2011}<2012^{73}-1=B\)
=>A<B
Nhân cả hai vế của A với 2012 , ta được :
2012A = 2012 + 20122 + 20123 + 20124 + .... + 201272 + 201273
=> 2012A - A = ( 2012 + 20122 + 20123 + 20124 + .... + 201272 + 201273 ) - ( 1 + 2012 + 20122 + 20123 + ... + 201271 + 201272 )
=> 2011A = 201273 - 1
=> A = ( 201273 - 1 ) : 2011
Vì ( 201273 - 1 ) : 2011 < 201273 - 1 nên A < B
A<B. Ai mk lại cho