Question

So sánh A và B:

\(A=\frac{10^{1992}+1}{10^{1991}+1}\)                       \(B=\frac{10^{1993}+1}{10^{1992+1}}\)

Answer 1

\(10A=\frac{10^{1993}+10}{10^{1993}+1}=1+\frac{9}{10^{1993}+1}\)

\(10B=\frac{10^{1994}+10}{10^{1994}+1}=1+\frac{9}{10^{1994}+1}\)

\(10^{1993}+1< 10^{1994}+1\Rightarrow\frac{9}{10^{1993}+1}>\frac{9}{10^{1994}+1}\)

\(\Rightarrow10A>10B\)

\(\Rightarrow A>B\)

Answer 2

Ta có B=\(\frac{10^{1993}+1}{10^{1992}+1}>\frac{10^{1993}+1+9}{10^{1992}+1+9}=\frac{10^{1993}+10}{10^{1992}+10}\)

        =  \(\frac{10\left(10^{1992}+1\right)}{10\left(10^{1991}+1\right)}=\frac{10^{1992}+1}{10^{1991}+1}=A\)

   =>      B > A

Answer 3

bạn Trần Thùy Dung sai rồi A và B nhân với 1:10