a) \(1=\frac{45}{46}+\frac{1}{46}\)

    \(1=\frac{2011}{2012}+\frac{1}{2012}\)

Vì \(\frac{1}{46}>\frac{1}{2012}\)\(\Rightarrow\)\(\frac{45}{46}< \frac{2011}{2012}\)

b)Vì 2010/2011 < 1 và 17/16 > 1 => 2010/2011 < 17/16

\(\dfrac{2010}{2011}\) và \(\dfrac{2011}{2012}\)

Ta có:

\(1-\dfrac{2010}{2011}=\dfrac{1}{2011}\)

\(1-\dfrac{2011}{2012}=\dfrac{1}{2012}\)

Vì \(\dfrac{1}{2011}>\dfrac{1}{2012}\) nên \(\dfrac{2010}{2011}< \dfrac{2011}{2012}\)

20112010​ và 2011201220122011​

Ta có:

1−20102011=120111−20112010​=20111​

1−20112012=120121−20122011​=20121​

Vì 12011>1201220111​>20121​ nên 20102011<2011201220112010​<20122011​

ta có: 1 - 2010/2011= 2011/2011 - 2010/2011=1/2011

           1 - 2011/2012= 2012/2012 - 2011/2012= 1/2012

   Vì 1/2011>1/2012

   Nên 2010/2011>2011/2012

\(A=\dfrac{-9\cdot10+\left(-19\right)}{10^{2011}}=\dfrac{-28}{10^{2011}}\)

\(B=\dfrac{-9\cdot10-19}{10^{2011}}=\dfrac{-109}{10^{2011}}\)

=>A>B

\(\frac{46}{45}=1+\frac{1}{45},\frac{2012}{2011}=1+\frac{1}{2011}\)

Có \(2011>45>0\Rightarrow\frac{1}{45}>\frac{1}{2011}\)

Do đó \(\frac{46}{45}>\frac{2012}{2011}\).

\(\frac{2011}{2010}>1>\frac{16}{17}\).

+ta có 10^2010=10...0(2010 số 0)

và 10^2011=10...0(2011 số 0)

suy ra  -9/10...0(2010 số 0)= -90/10...0(2011 số 0)[nhân tử,mẫu cho 10]

suy ra A=-90/10...0(2011 số 0)+-19/10...0(2011 số 0)= -109/10...0(2011 số 0)     [1]

+-19/10...0(2010 số 0)= -190/10...0(2011 số 0)[nhân tử,mẫu cho 10]

và 10^2011=10...0(2011 số 0)

suy ra -9/10...0(2011 số 0)+-190/10...0(2011 số 0)= -199/10...0(2011 số 0)    [2]

vì -109>-199 suy ra [1]>[2]

K CHO MIK VS BẠN ƠIIIIIIIIIIIIIIIIIII

\(-A=\frac{9}{10^{2010}}+\frac{19}{10^{2011}}\)

\(-A=\frac{9}{10^{2010}}+\frac{10}{10^{2011}}+\frac{9}{10^{2011}}\)

\(-A=\frac{9}{10^{2010}}+\frac{1}{10^{2010}}+\frac{9}{10^{2011}}\)

\(-A=\frac{10}{10^{2010}}+\frac{9}{10^{2011}}\)

\(-A=\frac{1}{10^{2009}}+\frac{9}{10^{2011}}\)

\(-B=\frac{9}{10^{2011}}+\frac{19}{10^{2010}}\)

Làm tương tự nhé 

ta thấy -b > -a nên a>b

#)Giải :

Ta có : \(1-\frac{2010}{2011}=\frac{1}{2011}\)

            \(1-\frac{2011}{2012}=\frac{1}{2012}\)

Vì \(\frac{1}{2011}>\frac{1}{2012}\Rightarrow\frac{2010}{2011}>\frac{2011}{2012}\)

\(\frac{2010}{2011}=1-\frac{1}{2011}\)

\(\frac{2011}{2012}=1-\frac{1}{2012}\)

\(2011\)<\(2012\)\(\Rightarrow\frac{1}{2011}\)>\(\frac{1}{2012}\)

\(\Rightarrow\frac{2010}{2011}\)<\(\frac{2011}{2012}\)

\(\frac{2010}{2011}=\frac{2011-1}{2011}=1-\frac{1}{2011}\)

\(\frac{2011}{2012}=\frac{2012-1}{2012}=1-\frac{1}{2012}\)

vì \(\frac{1}{2011}>\frac{1}{2012}\)nên \(\frac{2010}{2011}< \frac{2011}{2012}\)