cho A=1+2012+2012 mũ 2 + 2012 mũ 3+.............+2012 mũ 72 và B=2012 mũ 73 -1.so sánh A và B
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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)
\(G=1+2012+2012^2+2012^3+2012^4+...+2012^{71}+2012^{72}\)
\(\Rightarrow G=\dfrac{2012^{72+1}-1}{2012-1}\)
\(\Rightarrow G=\dfrac{2012^{73}-1}{2011}< H=2012^{73}-1\)
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a) 2011 . 2013 = 2011 . ( 2012 + 1 ) = 2011 . 2012 + 2011
20122 = 2012 . 2012 = ( 2011 + 1 ) . 2012 = 2011 . 2012 + 2012
Vì 2011 . 2012 + 2011 < 2011 . 2012 + 2012 nên 2011 . 2013 < 20122
![](https://rs.olm.vn/images/avt/0.png?1311)
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)
\(A=1+2012^1+2012^2+....+2012^{72}\\ \Rightarrow2012A=2012+2012^2+....+2012^{73}\\ \Rightarrow2011A=2012^{73}-1\\ \Rightarrow A=\frac{2012^{73}-1}{2011}\)
=> A<B
help me
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