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A=2001/2002+2002/2003
B=2001/2002+2003+2002/2002+2003
(tớ tách B ra đấy)
mà 2001//2002+2002/2003>2001/2002+2003+ 202/2002+2003
A>B
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Cách 1:\(\frac{2001}{2002}=1-\frac{1}{2002}\)
\(\frac{2002}{2003}=1-\frac{1}{2003}\)
Vì \(\frac{1}{2002}>\frac{1}{2003}\) nên \(\frac{2001}{2002}<\frac{2002}{2003}\)
Cách 2:Ta có:\(\frac{2001}{2002}<1\)
=>\(\frac{2001}{2002}<\frac{2001+1}{2002+1}=\frac{2002}{2003}\)
Vậy \(\frac{2001}{2002}<\frac{2002}{2003}\)
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ta có \(\frac{2000+2002}{2001+2003}\)= \(\frac{2000}{2001+2003}\)+ \(\frac{2002}{2001+2003}\)=\(\frac{2000}{4004}\)+\(\frac{2002}{4004}\)
ta có \(\frac{2000}{2001}\)>\(\frac{2000}{4004}\) và \(\frac{2002}{2003}\)> \(\frac{2002}{4004}\)
nên \(\frac{2000}{2001}\)+\(\frac{2002}{2003}\)>\(\frac{2000}{4004}\)+\(\frac{2002}{4004}\)
vậy \(\frac{2000}{2001}\)+\(\frac{2002}{2003}\)>\(\frac{2000+2002}{2001+2003}\)
\(\frac{2000+2002}{2001+2003}=\frac{2000}{2001+2003}+\frac{2002}{2001+2003}< \frac{2000}{2001}+\frac{2002}{2003}\)
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\(\dfrac{2001+2002}{2002+2003}< \dfrac{2001}{2002}+\dfrac{2002}{2003}\)
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Cách 1 :
Ta có :
2001/2002 = 4008003/4010006 ( quy đồng mẫu số )
2002/2003=4008004/4010006 ( quy đồng mẫu số )
Vì phân số 4008004/4010006 > 4008003/4010006 nên phân số 2001/2002 < 2002/2003
Cách 2 :
2001/2002 = 4006002/4008004 ( quy đồng tử số )
2002/2003 = 4006002/4008003 ( quy đồng tử số )
Vì 4006002/4008004 < 4006002/4008003 nên phân số 2001/2002 < 2002/2003
Cách 3 :
2001/2002 = 1 - 1/2002
2002/2003 = 1 - 1/2003
Vì 1/2002 > 1/2003 nên 2001/2002 < 2002/2003
2001/2002=1-1/2002
2002/2003=1-1/2003
vi 1/2003<1/2002 nen 2001/2002<2002/2003
Ta có: 2003 x 2001 < 2002 x 2002
=> \(\frac{2001}{2002}\)<\(\frac{2002}{2003}\)