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2000/2001 * 2002/2003 * 2001/2002 * 2003/2004*2006/2000
=((2000/2001).2002):2003.2001/2002).2003):2004.2006)/2000
=1.000998004
\(\dfrac{2000}{2001}\cdot\dfrac{2002}{2003}\cdot\dfrac{2001}{2002}\cdot\dfrac{2003}{2004}\cdot\dfrac{2006}{2000}=\dfrac{2006}{2004}=\dfrac{1003}{1002}\)
\(\frac{2006}{2008}\times\frac{2001}{2004}\times\frac{2008}{2002}\times\frac{2004}{2006}\times\frac{1001}{2001}=\frac{2006.2001.2008.2004.1001}{2008.2004.2002.2006.2001}\)
\(=\frac{\left(2001.2004.2006.2008.\right).1001}{\left(2001.2004.2006.2008\right).2002}=\frac{1001}{2002}=\frac{1001.1}{1001.2}=\frac{1}{2}\)
\(\frac{2001}{2000}-\frac{2002}{2001}=\frac{2001.2001}{2000.2001}-\frac{2002.2000}{2000.2001}\)
\(=\frac{\left(2002-1\right).\left(2000+1\right)-2002.2000}{2000.2001}\)
\(=\frac{2002.\left(2000+1\right)-\left(2000+1\right)-2002.2000}{2000.2001}\)
\(=\frac{2002.2000+2002-2000-1-2002.2000}{2000.2001}\)
\(=\frac{2002.2000+1-2002.2000}{2000.2001}\)
\(=\frac{1}{2000.2001}\)
Tinh nhanh
2003×14+1998+2001×2002 / 2002+2002×503+504×2003
Viet ro loi giai nhe! Ai nhanh mk tk cho!
2003x14+1998+2001x2002/2002+2002x503+504x2003 =2003x14+1998+2001x1+2002x503+504x2003 =2003x14+1998+2001+2002x503+504x2003 =28042+1998+2001+1007006+1009512 =(28042+1009512+1007006)+1998+2001 =2044560+1998+2001=2048559 TK MIk nha bn! mk tra loi dau tien ma ! Giu loi hua nhe!
2003 x 14 + 1988 + 2001 x 2002
=28042 + 1988 + 4006002
=4036032
2002 + 2002 x 503 +504 x 2002
=2002 x 1 + 2002 x 503 + 504 x 2002
=2002 x (1 + 503 + 504)
=2002 x 908
=1817816
Ta có:
B=\(\frac{2000+2001}{2001+2002}=\frac{2000}{2001+2002}+\frac{2001}{2001+2002}\)
Do \(\frac{2000}{2001}>\frac{2000}{2001+2002};\frac{2001}{2002}>\frac{2001}{2001+2002}\)
\(\Rightarrow\frac{2000}{2001}+\frac{2001}{2002}>\frac{2000}{2001+2002}+\frac{2001}{2001+2002}\)
\(\Rightarrow A>B\)
Vậy \(A>B\)
Ta có:$B=\frac{2000}{2001+2002}+\frac{2001}{2001-2002}$B=20002001+2002 +20012001−2002
Vì:$\frac{2000}{2001}>\frac{2000}{2001+2002}$20002001 >20002001+2002
$\frac{2001}{2002}>\frac{2001}{2001+2002}$20012002 >20012001+2002
$\Rightarrow\left(\frac{2000}{2001}+\frac{2001}{2002}\right)>\left(\frac{2000}{2001-2002}-\frac{2001}{2001+2001}\right)$⇒(20002001 +20012002 )>(20002001−2002 −20012001+2001 )
$\Rightarrow A>B$⇒A>B
............=2000000001