Question

so sánh \(A=\dfrac{10^{17}+1}{10^{18}+1}\)

\(B=\dfrac{10^{18}+1}{10^{19}+1}\)

Answer 1

Do \(\dfrac{10^{18}+1}{10^{19}+2}< 1\Rightarrow B< \dfrac{10^{18}+1+9}{10^{19}+1+9}\)

\(\Rightarrow B< \dfrac{10^{18}+10}{10^{19}+10}\)

\(\Rightarrow B< \dfrac{10\left(10^{17}+1\right)}{10\left(10^{18}+1\right)}\)

\(\Rightarrow B< \dfrac{10^{17}+1}{10^{18}+1}\)

\(\Rightarrow B< A\)