Tính chất: \(\dfrac{a}{b}< \dfrac{a+m}{b+m}\)
b) \(B=\dfrac{10^{1001}+1}{10^{1002}+1}< \dfrac{10^{1001}+10}{10^{1002}+10}\)
\(B< \dfrac{10\left(10^{1000}+1\right)}{10\left(10^{1001}+1\right)}\)
\(B< \dfrac{10^{1000}+1}{10^{1001}+1}\)
\(B< A\)
c) \(A=\dfrac{10^{2024}+1}{10^{2023}+1}< \dfrac{10^{2024}+10}{10^{2023}+10}\)
\(A< \dfrac{10\left(10^{2023}+1\right)}{10\left(10^{2022}+1\right)}\)
\(A< \dfrac{10^{2023}+1}{10^{2022}+1}\)
\(A< B\)
c) \(B=\dfrac{10^{1001}+1}{10^{1000}+1}< \dfrac{10^{1001}+10}{10^{1000}+10}\)
\(B< \dfrac{10\left(10^{1000}+1\right)}{10\left(10^{999}+1\right)}\)
\(B< \dfrac{10^{1000}+1}{10^{999}+1}\)
\(B< A\)
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