a: \(10A=\dfrac{10^{2021}+10}{10^{2021}+1}=1+\dfrac{9}{10^{2021}+1}\)
\(10B=\dfrac{10^{2022}+10}{10^{2022}+1}=1+\dfrac{9}{10^{2022}+1}\)
mà 10^2021+1<10^2022+1
nên A>B
b: \(A=\dfrac{1}{2}\left(\dfrac{4}{1\cdot5}+\dfrac{6}{5\cdot11}+...+\dfrac{12}{29\cdot41}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{11}+...+\dfrac{1}{29}-\dfrac{1}{41}\right)=\dfrac{20}{41}\)
\(B=\dfrac{1}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{6}{4\cdot10}+\dfrac{9}{10\cdot19}+\dfrac{12}{19\cdot31}\right)\)
=1/3(1-1/4+1/4-1/10+...+1/19-1/31)
=1/3*30/31=10/31=20/62
=>A>B
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