\(3A.\\ A=\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)...\left(\dfrac{1}{10}-1\right)\\ =\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot\dfrac{-3}{4}\cdot...\cdot\dfrac{-9}{10}\\ =\dfrac{-1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{9}{10}\\ =\dfrac{-1}{10}>\dfrac{-1}{9}\)
\(3B.\\ B=\left(\dfrac{1}{4}-1\right)\left(\dfrac{1}{9}-1\right)...\left(\dfrac{1}{100}-1\right)\\ =-\dfrac{3}{4}\cdot\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot...\cdot\dfrac{99}{100}\\ =-\dfrac{3\cdot2\cdot4\cdot3\cdot5\cdot...\cdot9\cdot11}{2^2\cdot3^2\cdot4^2\cdot...\cdot10^2}\\ =-\dfrac{2\cdot\left(3^2\cdot4^2\cdot...\cdot9^2\right)\cdot10\cdot11}{2^2\cdot\left(3^2\cdot4^2\cdot...\cdot9^2\right)\cdot10^2}\\ =-\dfrac{2\cdot10\cdot11}{2^2\cdot10^2}\\ =\dfrac{-11}{20}< \dfrac{-11}{21}\)
