\(A=\frac{2010\times2011-1005}{2010\times2010+1005}\)

\(A=\frac{2010\times\left(2010+1\right)-1005}{2010\times2010+1005}\)

\(A=\frac{2010\times2010+2010-1005}{2010\times2010+1005}\)

\(A=\frac{2010\times2010+1005}{2010\times2010+1005}\)

\(A=1\)

\(A=\frac{2010\times2011-1005}{2010\times2010+1005}\)

\(A=\frac{4042110-1005}{4040100+1005}\)

\(A=\frac{4041105}{4041105}\)

\(A=1\)

\(A=\frac{2010\times2011-1005}{2010\times2010+1005}\)

\(\Rightarrow A=\frac{1005\times2\times2011-1005}{1005\times2\times2010+1005}\)

\(\Rightarrow A=\frac{1005\times\left(2\times2011-1\right)}{1005\times\left(2\times2010+1\right)}\)

\(\Rightarrow A=\frac{2\times2011-1}{2\times2010+1}=\frac{4021}{4021}=1\)

\(=\frac{\left(2009-1\right)\cdot2009+2000}{2009\cdot\left(2009+1\right)-2018}=\frac{2009^2-9}{2009^2-9}=1\\ \)

\(A=\frac{2009x2010+2000}{2011x2010-2020}=\frac{2009x2010+2000}{2009x2010+2x2010-2020}=\frac{2009x2010+2000}{2009x2010+4020-2020}=\frac{2000}{4020-2020}=\frac{2000}{2000}=1\)

Nhấn đúng cho mk nha!!!!!!!!!!

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

\(t=\frac{2009.2010+2000}{2011.2010-2020}\)

\(t=\frac{2009.2010+2000}{\left(2009+2\right).2010-2020}\)

\(t=\frac{2009.2010+2000}{2009.2010+2.2010-2020}\)

\(t=\frac{2009.2010+2000}{2009.2010+2000}=1\)

\(q=\frac{\text{2014.2015+2010}}{2016.2015-2020}\)

\(q=\frac{\text{2014.2015+2010}}{\left(2014+2\right).2015-2020}\)

\(q=\frac{\text{2014.2015+2010}}{2014.2015+2.2015-2020}\)

\(q=\frac{\text{2014.2015+2010}}{\text{2014.2015+2010}}=1\)

\(\text{ta có : }A=\frac{2009.2010-1}{2009.2010}=\frac{2009.2010}{2009.2010}-\frac{1}{2009.2010}=1-\frac{1}{2009.2010}\)

\(B=\frac{2010.2011-1}{2010.2011}=\frac{2010.2011}{2010.2011}-\frac{1}{2010.2011}=1-\frac{1}{2010.2011}\)

\(\text{Vì }2009.2010\frac{1}{2010.2011}\)

Hay A<B