Tính nhanh .\(\frac{2009x2010+20}{2010x2010-1990}\)
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\(A=\frac{2010\times2011-1005}{2010\times2010+1005}\)
\(A=\frac{2010\times\left(2010+1\right)-1005}{2010\times2010+1005}\)
\(A=\frac{2010\times2010+2010-1005}{2010\times2010+1005}\)
\(A=\frac{2010\times2010+1005}{2010\times2010+1005}\)
\(A=1\)
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\(=\frac{\left(2009-1\right)\cdot2009+2000}{2009\cdot\left(2009+1\right)-2018}=\frac{2009^2-9}{2009^2-9}=1\\ \)
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\(A=\frac{2009x2010+2000}{2011x2010-2020}=\frac{2009x2010+2000}{2009x2010+2x2010-2020}=\frac{2009x2010+2000}{2009x2010+4020-2020}=\frac{2000}{4020-2020}=\frac{2000}{2000}=1\)
Nhấn đúng cho mk nha!!!!!!!!!!
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1/3.4 + 1/4.5+ 1/5.6 +...... + 1/2009.2010
= 1/3 -1/4+1/4-1/5 +1/5-1/6+....+1/2009-1/2010
= 1/3 - 1/2010
= 223/670
1/3.4+1/4x5+1/5x6+............+1/2009x2010
=1/3+1/4-1/4+1/5-1/5+1/6+.........+1/2009-1/2010
=1/3-1/2010
=223/670
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\(t=\frac{2009.2010+2000}{2011.2010-2020}\)
\(t=\frac{2009.2010+2000}{\left(2009+2\right).2010-2020}\)
\(t=\frac{2009.2010+2000}{2009.2010+2.2010-2020}\)
\(t=\frac{2009.2010+2000}{2009.2010+2000}=1\)
\(q=\frac{\text{2014.2015+2010}}{2016.2015-2020}\)
\(q=\frac{\text{2014.2015+2010}}{\left(2014+2\right).2015-2020}\)
\(q=\frac{\text{2014.2015+2010}}{2014.2015+2.2015-2020}\)
\(q=\frac{\text{2014.2015+2010}}{\text{2014.2015+2010}}=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\text{ta có : }A=\frac{2009.2010-1}{2009.2010}=\frac{2009.2010}{2009.2010}-\frac{1}{2009.2010}=1-\frac{1}{2009.2010}\)
\(B=\frac{2010.2011-1}{2010.2011}=\frac{2010.2011}{2010.2011}-\frac{1}{2010.2011}=1-\frac{1}{2010.2011}\)
\(\text{Vì }2009.2010\frac{1}{2010.2011}\)
Hay A<B
\(\frac{2009x2010+20}{2009x2010-1990}\)
=\(\frac{2009x2010+20}{2009x2010+2010-1990}\)
=\(\frac{2009x2010+20}{2009x2010+20}\)
\(\frac{2009+20}{2010-1990}=\frac{2029}{20}=>\frac{2009x2010+20}{2010x2010-1990}=\frac{2029}{20}\)