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a, \(A=2^0+2^1+2^2+...+2^{2010}\)
\(=>2A=2^1+2^2+2^3+...+2^{2011}\)
\(=>2A-A=\left(2^1+2^2+2^3+...+2^{2011}\right)-\left(2^0+2^1+2^2+...+2^{2010}\right)\)
\(=>2A=2^{2011}-2^0=2^{2011}-1\)
Vì \(2^{2011}-1=2^{2011}-1\)
\(=>A=B\)
a) Ta có : A=1+2+22+...+22010
2A=2+22+23+...+22011
\(\Rightarrow\) 2A-A=(2+22+23+...+22011)-(1+2+22+...+22010)
\(\Rightarrow\) A=22011-1
Mà B=22011-1
\(\Rightarrow\)A=B
Vậy A=B.
b) Ta có : A=2009.2011
B=20102=2010.2010
\(\Rightarrow\)A=2009.2010+2009
B=2009.2010+2010
Vì 2009<2010 nên 2009.2010+2009<2009.2010+2010
hay A<B
Vậy A<B.
A = 2009.2010 < 2010.2010 = B
Vậy A < B
Câu b:
A = 1030 = (103)10 = 100010
B = 2100 = (210)10 = 102410
1000 < 2014 < = > 100010 < 102410
VẬy A < B
a)B=20102=2010*2010
Vì 2009<2010 nên 2009*2010<2010*2010 hay A<B
b)A=1030=(103)10=100010
B=2100=(210)10=102410
Vì 1000<1024 nên 100010<102410 hay A<B
A=2009.2011=(2010-1).2011=2010.2011-2011
B=2010.2010=2010.(2011-1)=2010.2011-2010
dO 2010.2011=2010.2011 NHƯNG 2011>2010 NÊN 2010.2011-2011<2010.2011-2010
VẬY A<B
A=20+21+22+...+22010
=>2A=21+22+23+...+22011
=>2A-A=(21+22+23+...+22011)-(20+21+22+...+22010)
=>A=22011-1=B
Vậy A=B
A = 20 + 21 + ..... + 22010
2A = 21 + 22 + ..... + 22011
2A - A = 22011 - 1
Mà B = 22011 - 1
=> A = B
A= 1030 = (103 ) 10 = 100010
B= 2100 = (210 ) 10 = 102410
Vì 100010 < 102410
=> A<B
A=1030=(103)10=100010
B=2100=(210)10=102410
Vì 100010<102410 nên A<B
a) 8180 < 2790
b) 377 > 738
c) 536 < 1124
d) 291 < 535
Đúng thì k, sai thì thôi
A=2020^10+2/2020^11+2
⇒ 2020A=2020^11+2.2020/2020^11+2
= 1+2.2020−2/2020^11+2
B=2020^11+2/2020^12+2
⇒ 2020B=2020^12+2.2020/2020^12+2
= 1+2.2020−2/2020^12+2
Vì 2020^12+2>2020^11+2
⇒ 2.2020−2/2020^11+2<2.2020−2/2020^12+2
⇒ 2020A<2020B
⇒ A<B
A=2009.2011=2009.(2010+1)=2009.2010+2009
B=20102=(2009+1).2010=2009.2010+2010
Vì 2009<2010 nên: A<B
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