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\(\dfrac{4}{17}=\dfrac{16}{68}\\ Vì:\dfrac{16}{68}< \dfrac{16}{63}\Rightarrow\dfrac{4}{17}< \dfrac{16}{63}\\ ---\\ \dfrac{1007}{1009}=1-\dfrac{2}{1009};\dfrac{1005}{1007}=1-\dfrac{2}{1007}\\ Vì:\dfrac{2}{1009}< \dfrac{2}{1007}\Rightarrow1-\dfrac{2}{1009}>1-\dfrac{2}{1007}\\ \Rightarrow\dfrac{1007}{1009}>\dfrac{1005}{1007}\)
a: 4/17=16/68
16/68<16/63
=>4/17<16/63
b: 19/53<20/53
20/53<20/50(Vì 53>50)
=>19/53<20/50=2/5
mà 2/5=30/75<30/73
nên 19/53<30/73
c: 1007/1009=1-2/1009
1005/1007=1-2/1007
1009>1007
=>2/1009<2/1007
=>-2/1009>-2/1007
=>1007/1009>1005/1007
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Ta có: 20082 > 20082 -1 = 2007.2009 => 1007/1008<1008/1009
Ta có:\(\frac{1007}{1008}=1-\frac{1}{1008}\)
\(\frac{1008}{1009}=1-\frac{1}{1009}\)
mà \(\frac{1}{1008}>\frac{1}{1009}\)
=> \(1-\frac{1}{1008}< 1-\frac{1}{1009}\)
Hay \(\frac{1007}{1008}< \frac{1008}{1009}\)
Vậy .......
Chúc bạn hk tốt!!! nhớ k cho mình na
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Ta có :
\(1-\frac{1006}{1007}=\frac{1}{1007}=\frac{2}{2014}\)
\(1-\frac{2013}{2015}=\frac{2}{2015}\)
Ta thấy :
\(\frac{2}{2014}>\frac{2}{2015}\Rightarrow1-\frac{1006}{1007}< 1-\frac{2013}{2015}\)
Mà \(1=1\)
Vậy \(\frac{1006}{1007}< \frac{2013}{2015}\)
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\(1-\frac{1003}{1005}=\frac{2}{1005}>\frac{2}{1007}=1-\frac{1005}{1007}\Rightarrow\frac{1003}{1005}
ta có : 1-1003/1005=2/1005
1-1005/1007=2/1007
vì 2/1005>2/1007 nên 1003/1005<1005/1007
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VÌ A = 1/2010 > 1/2011 > 1/2012 (1)
B = 1/2009 <1/1007 (2)
TỪ (1) VÀ (2) => 1/2010 < 1/1007
VẬY A < B
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C = 1.2.3.4....2011
D = 1007/2 . 1008/2 . 1009/2.....2012/2
D = (1007.1008.1009.....2012) : (2.2.2.2........2) (có 2012 - 1007 + 1 = 1006 số 2 )
D = (1007.1008.1009....503 .2.2) : 21004
MÀ (4.503.1007.1008.....2011) < (1.2.3.....2011)
Vậy c > D
90^8<100^7
Ta có:
90^8=(10.9)^8=10^72
100^7=(10.10)^7=10^70
Vì 10^72>10^70 nên 90^8>100^7
Vậy 90^8>100^7