\(A=\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)...\left(\dfrac{1}{10}-1\right)=\dfrac{-1}{2}.\dfrac{-2}{3}...\dfrac{-9}{10}=\dfrac{-1}{10}>\dfrac{-1}{9}\)
\(B=\left(\dfrac{1}{4}-1\right)\left(\dfrac{1}{9}-1\right)...\left(\dfrac{1}{100}-1\right)=\dfrac{-3}{2^2}.\dfrac{-8}{3^2}...\dfrac{-99}{10^2}=-\left(\dfrac{1.3}{2^2}.\dfrac{2.4}{3^2}...\dfrac{9.11}{10^2}\right)=-\left(\dfrac{1.2...9}{2.3...10}.\dfrac{3.4...11}{2.3...10}\right)=-\left(\dfrac{1}{10}.\dfrac{11}{2}\right)=-\dfrac{11}{20}< -\dfrac{11}{21}\)
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