so sanh A va B
A= (2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)
B=2^32
Những câu hỏi liên quan
1)so sanh : a=10^41-1/10^42-1 va b=10 ^ 40 -1 /40^11+1 .
2)ct: 1/2-1/4+1/8-1/16+1/32-1/64
1)so sanh : a=10^41-1/10^42-1 va b=10 ^ 40 -1 /40^11+1 .2)ct: 1/2-1/4+1/8-1/16+1/32-1/64<1/3
so sánh :a)A=2015.2017 va B=2016^2
b)C=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1) va D=2^32
a ) \(A=2015.2017=\left(2016-1\right)\left(2016+1\right)=2016^2-1\)
Do \(2016^2>2016^2-1\)
\(\Rightarrow B>A\)
b ) \(C=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)
\(=2^{32}-1< 2^{32}=D\)
Vậy \(C< D\)
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so sánh :a)A=2015.2017 va B=20162
Ta có: A = 2015.2017 = (2016-1)(2016+1)
= 20162-1<20162
=> A < B
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so sanh \(A=3.\left(2^2+1\right).\left(2^4+1\right).\left(2^8+1\right).\left(2^{16}+1\right).\left(2^{32}+1\right)\)
va \(B=2^{64}\)
c tánh 3 là 2^2-1 sau đó áp dụng HDT thứ 3 là ra
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So sanh: A va B
A= 2*(3+1)(32+1)...(316+1)
B= 332
So sanh :
A = 1/2 + 1/4+ 1/8 + 1/16 + 1/32 voi 2005/2006
A = 31/32
Ta có 1 - 31/32 = 1/32
1 - 2005/2006 = 1/2006
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a. So sanh 2 phan so:A= 2015/2016+2016/2017+2017/2018 va B = 2015+2016+2017/2016+2017+2018
b.1/2.4+1/4.6+........+1/(2x-2).2x = 1/8
c.Cho A = 1/4+1/9+1/16+...+1/81+1/100 . Chung minh rang : A > 65/132
d.Cho B = 12/(2 . 4 ) ^ 2 + 20/ (4 . 6) ^2 + ...........+ 388/ ( 96 . 98 ) ^ 2 + 396/ ( 98 . 100 ) ^2 .Hay so sanh B voi 1 /4
So sanh 2 so sau:
A=332 -1
B=(3+1) .(32 +1) .(34 +1) . (38 +1) .(316 +1)
B = (3 + 1).(32 + 1).(34 + 1).(38 + 1).(316 + 1)
2B = (3 - 1).(3 + 1).(32 + 1).(34 + 1).(38 + 1).(316 + 1)
= (32 - 1).(32 + 1).(34 + 1).(38 + 1).(316 + 1)
= (34 - 1).(34 + 1).(38 + 1).(316 + 1)
= (38 - 1).(38 + 1).(316 + 1)
= (316 - 1).(316 + 1)
= 332 - 1
Vậy A = B
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so sanh bang cach van dunghang dang thuc A=2 \(^{16}\)va B=(2+1)(2\(^2\)+1)(2\(^4\)+1)(2\(^8\)+1)
Ta có : \(B=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)=2^{16}-1=A-1\)
Vậy B < A
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