a: \(10A=\dfrac{10^{201}+10}{10^{201}+1}=1+\dfrac{9}{10^{201}+1}\)
\(10B=\dfrac{10^{202}+10}{10^{202}+1}=1+\dfrac{9}{10^{202}+1}\)
Vì \(10^{201}+1< 10^{202}+1\)
nên \(\dfrac{9}{10^{201}+1}>\dfrac{9}{10^{202}+1}\)
=>\(\dfrac{9}{10^{201}+1}+1>\dfrac{9}{10^{202}+1}+1\)
=>10A>10B
=>A>B
b: \(A=\dfrac{10^{2024}}{10^{2024}-5}=\dfrac{10^{2024}-5+5}{10^{2024}-5}=1+\dfrac{5}{10^{2024}-5}\)
\(B=\dfrac{10^{2024}+1}{10^{2024}-4}=\dfrac{10^{2024}-4+5}{10^{2024}-4}=1+\dfrac{5}{10^{2024}-4}\)
Ta có: \(10^{2024}-5< 10^{2024}-4\)
=>\(\dfrac{5}{10^{2024}-5}>\dfrac{5}{10^{2024}-4}\)
=>\(1+\dfrac{5}{10^{2024}-5}>1+\dfrac{5}{10^{2024}-4}\)
=>A>B
m: \(A=\dfrac{17^{2024}+3}{17^{2024}-1}=\dfrac{17^{2024}-1+4}{17^{2024}-1}=1+\dfrac{4}{17^{2024}-1}\)
\(B=\dfrac{17^{2024}}{17^{2024}-4}=\dfrac{17^{2024}-4+4}{17^{2024}-4}=1+\dfrac{4}{17^{2024}-4}\)
Ta có: \(17^{2024}-1>17^{2024}-4\)
=>\(\dfrac{4}{17^{2024}-1}< \dfrac{4}{17^{2024}-4}\)
=>\(1+\dfrac{4}{17^{2024}-1}< 1+\dfrac{4}{17^{2024}-4}\)
=>A<B
