Ta có : \(10.A=\frac{10^{2017}+10}{10^{2017}+1}=\frac{10^{2017}+1+9}{10^{2017}+1}=\frac{10^{2017}+1}{10^{2017}+1}+\frac{9}{10^{2017}+1}=1+\frac{9}{10^{2017}+1}\)

\(10.B=\frac{10^{2018}+10}{10^{2018}+1}=\frac{10^{2018}+1+9}{10^{2018}+1}=\frac{10^{2018}+1}{10^{2018}+1}+\frac{9}{10^{2018}+1}=1+\frac{9}{10^{2018}+1}\)

Vì \(1=1\)và \(\frac{9}{10^{2017}+1}>\frac{9}{10^{2018}+1}\)nên \(1+\frac{9}{10^{2017}+1}>1+\frac{9}{10^{2018}+1}\)hay \(A>B\)

Vậy \(A>B\)

a hơn b

a hơn b

a hơn b 

chúc học giỏi

A>B do A>4 cònB<4

Nhân cả hai tử của \(A\)và \(B\)với 2 , ta được :

\(10A=10.\left(\frac{10^{2016}+1}{10^{2017}+1}\right)=\frac{10^{2017}+1+9}{10^{2017}+1}=1+\frac{9}{2^{2017}+1}\)

\(10B=10\left(\frac{10^{2017}+1}{10^{2018}+1}\right)=\frac{10^{2018}+10}{10^{2018}+1}=\frac{10^{2018}+1+9}{10^{2018}}=1+\frac{9}{10^{2018}+1}\)

Vì \(1=1;9=9\)

\(\Rightarrow\)Ta so sánh mẫu , ta có:

\(10^{2017}< 10^{2018}\)

\(\Rightarrow10^{2017}+1< 10^{2018}+1\)

\(\Rightarrow1+\frac{9}{10^{2017}+1}>1+\frac{9}{10^{2018}+1}\)

\(\Rightarrow10A>10B\)

Hay \(A>B\)

\(A=\frac{10^{2016}+1}{10^{2017}+1}\)

\(A=\frac{10^{2016}+1}{10^{2017}+1}+\frac{10^{2017}+1}{10^{2017}+1}\)

\(A=\frac{10^{2016}+1+10^{2017}+1}{10^{2017}+1}\)

\(A=\frac{10^{2016}+10^{2017}+1+1}{10^{2016}.10+1}\)

\(A=\frac{10^{2016}.\left(1+10\right)+2}{10^{2016}.10+1}\)

\(A=\frac{10^{2016}.11+2}{10^{2016}.10+1}\)

\(A=\frac{11+2}{10+1}\)

\(A=\frac{13}{11}\)(1)

Làm tương tự phần B

Từ 1 và 2 

\(\Leftrightarrow\)\(\frac{13}{11}=\frac{13}{11}\)

\(\Leftrightarrow\)A = B

Ta có :

A = \(\frac{10^{2017}+1}{10^{2018}+1}\)< 1 => A < \(\frac{10^{2017}+1+9}{10^{2018}+1+9}\)= \(\frac{10^{2017}+10}{10^{2018}+10}\)= \(\frac{10^{2016}+1}{10^{2017}+1}\)= B

Vậy A < B

A<B. lời giải thích khó viết lắm nên bạn tự tìm cách làm nhé

Ta có :  \(A=\frac{10^{2016}+1}{10^{2017}+1}\) 

Suy ra  \(10A=\frac{10^{2017}+10}{10^{2017}+1}\) 

Suy ra  \(10A=1+\frac{9}{10^{2017}+1}\) 

Ta lại có : \(B=\frac{10^{2017}+1}{10^{2018}+1}\) 

Suy ra : \(10B=\frac{10^{2018}+10}{10^{2018}+1}\) 

Suy ra : \(10B=1+\frac{9}{10^{2018}+1}\) 

Vì  \(\frac{9}{10^{2017}+1}>\frac{9}{10^{2018}+1}\) 

Nên  \(1+\frac{9}{10^{2017}+1}>1+\frac{9}{10^{2018}+1}\) 

Suy ra \(10A>10B\) 

Suy ra \(A>B\)

\(B< \frac{10^{2017}+1+9}{10^{2018}+1+9}=\frac{10^{2017}+10}{10^{2018}+10}=\frac{10\left(10^{2016}+1\right)}{10\left(10^{2017}+1\right)}=\frac{10^{2016}+1}{10^{2017}+1}=A\)

vậy A > B

Ta có: \(\hept{\begin{cases}A=\frac{10^{2016}+1}{10^{2017}+1}\\B=\frac{10^{2017}+1}{10^{2018}+1}\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}10A=\frac{10^{2017}+10}{10^{2017}+1}=\frac{10^{2017}+1+9}{10^{2017}+1}=1+\frac{9}{10^{2017}+1}\\10B=\frac{10^{2018}+10}{10^{2018}+1}=\frac{10^{2018}+1+9}{10^{2018}+1}=1+\frac{9}{10^{2018}+1}\end{cases}}\)

Vì \(\frac{9}{10^{1017}+1}>\frac{9}{10^{2018}+1}\)

nên \(10A>10B\Rightarrow A>B\)

\(A=\frac{10^{2016}+1}{10^{2017}+1}\Rightarrow10A=\frac{10\cdot(10^{2016}+1)}{10^{2017}+1}=\frac{10^{2017}+10}{10^{2017}+1}\)

\(A=\frac{10^{2017}+1+9}{10^{2017}+1}=\frac{10^{2017}+1}{10^{2017}+1}+\frac{9}{10^{2017}+1}=1+\frac{9}{10^{2017}+1}\)

Vì \(10^{2016}+1< 10^{2017}+1\)

\(\Rightarrow\frac{9}{10^{2016}+1}>\frac{9}{10^{2017}+1}\)

\(\Rightarrow\)\(1+\frac{9}{10^{2016}+1}>1+\frac{9}{10^{2017}+1}\)

....

A= \(\frac{10^{2016}+1}{10^{2016}+1}=\frac{10^{2016}+1}{10\cdot10^{2016}+1}=\frac{1}{10}\cdot\frac{10^{2016}+1}{10^{2016}+1}=\frac{1}{10}\)(1)

B=\(\frac{10^{2017}+1}{10^{2018}+1}=\frac{10^{2017}+1}{10\cdot10^{2017}+1}=\frac{1}{10}\cdot\frac{10^{2017}+1}{10^{2017}+1}=\frac{1}{10}\)(2)

Từ (1) và (2) \(\Rightarrow\)A=B