Ta có:2012/2010=1+1/2011+1/2012 (1)

Thay (1) vào A, ta có:

2010/2011+2011/2012+1+1/2011+1/2012

= (2010/2011+1/2011) + 1+ (2011/2012+1/2012)

=1+1+1=3=51/17

suy ra A>51/17

Ta có B=1/3+1/4+...+1/17(có 15 sh)

B=(1/17+1/3).15:2

B=50/17(2)

Từ (1) và (2)=>A>B

a) \(A=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)=\dfrac{1}{2}\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)=\dfrac{1}{2}\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)=\dfrac{1}{2}\left(3^{32}-1\right)< 3^{32}-1=B\)

b) \(A=2011.2013=\left(2012-1\right)\left(2012+1\right)=2012^2-1< 2012^2=B\)

A=(2011x2011+1)/(2012x2011-2010)

=(2011x2011+1)/[(2011+1)x2011-2010]

=(2011x2011+1)/(2011x2011+1x2011-2010)

=(2011x2011+1)/(2011x2011+1)=1

A=1<2012/2011=B

nên A<B

\(10A=\frac{2012^{2013}+10}{2012^{2013}+1}=\frac{2012^{2013}+1+9}{2012^{2013}+1}=1+\frac{9}{2012^{2013}+1}\)

\(10B=\frac{2012^{2012}+10}{2012^{2012}+1}=\frac{2012^{2012}+1+9}{2012^{2012}+1}=1+\frac{9}{2012^{2012}+1}\)

Vì \(\frac{9}{2012^{2013}+1}

ta co A=\(\frac{2012^{2012}+1}{2012^{2013}+1}< \frac{2012^{2012}+1+2011}{2012^{2013}+1+2011}\)=\(\frac{2012^{2012}+2012}{2012^{2013}+2012}=\frac{2012\left(2012^{2011}+1\right)}{2012\left(2012^{2012}+1\right)}\)

           =>A<B

la lớn

I doNt know