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

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

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

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

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

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

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

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

a,A=2^0+2^1+2^2+...+2^2014

2A=2^1+2^2+2^3+...+2^2015

2A-A=(2^1+2^2+2^3+...+2^2015)-(2^0+2^1+2^2+...+2^2014)

A=2^2015-2^0=2^2015-1=B

=>A=B

b,A=2014.2016=2014.(2015+1)=2014.2015+2014

B=2015^2=2015.2015=(2014+1).2015=2014.2015+2015

Vì 2014<2015 => A<B.

A  = 6.(1/1.3+1/3.5+...+1/2015.2017)

   = 6.(1/1-1/3+1/3-1/5+...+1/2015-1/2017)

   = 6.(1/1-1/2017)

   = 6.2016/2017

   =12096/2017

\(\frac{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}{\frac{2013}{1}+\frac{2014}{2}+\frac{2015}{3}+...+\frac{4024}{2012}-2012}\)

\(=\frac{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}{\left(\frac{2013}{1}-1\right)+\left(\frac{2014}{2}-1\right)+\left(\frac{2015}{3}-1\right)+...+\left(\frac{4024}{2012}-1\right)}\)

\(=\frac{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}{\frac{2012}{1}+\frac{2012}{2}+\frac{2012}{3}+...+\frac{2012}{2012}}\)

\(=\frac{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}{2012.\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}\right)}\)

\(=\frac{1}{2012}\)

Ủng hộ mk nha ^_-

Ta có : 

\(A=\frac{1}{2016.2015}+\frac{1}{2015.2014}+\frac{1}{2014.2013}+...+\frac{1}{2}\)

\(A=\frac{1}{1.2}+...+\frac{1}{2013.2014}+\frac{1}{2014.2015}+\frac{1}{2015.2016}\)

\(A=\frac{1}{1}-\frac{1}{2}+...+\frac{1}{2013}-\frac{1}{2014}+\frac{1}{2014}-\frac{1}{2015}+\frac{1}{2015}-\frac{1}{2016}\)

\(A=1-\frac{1}{2016}\)

\(A=\frac{2015}{2016}\)

Vậy \(A=\frac{2015}{2016}\)

Chúc bạn học tốt ~ 

ai kb vs tôi ko

Mình giúp bạn nha!

A = 2017/1 + 2017/2 + 2017/3 + . . . + 2017/2018   /   2017/1 + 2016/2 + 2015/3 + . . .+ 1/2017

    = 2017 . ( 1 + 1/2 + 1/3 + . . . +1/2018 )   /   ( 2017 . 2016 . 2015 . . . 1) . ( 1 + 1/2 + 1/3 +. . . + 1/2017 )

    = 1/2016 . 2015 . 2014. . . 1

k mình nha

Dễ mà, bạn hãy suy nghĩ đi