Bài 2:
\(a.\dfrac{1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}}{1-\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{16}}\\ =\dfrac{\dfrac{16}{16}+\dfrac{8}{16}+\dfrac{4}{16}+\dfrac{2}{16}+\dfrac{1}{16}}{\dfrac{16}{16}-\dfrac{8}{16}+\dfrac{4}{16}-\dfrac{2}{16}+\dfrac{1}{16}}\\ =\dfrac{31}{16}:\dfrac{11}{16}\\ =\dfrac{31}{16}\cdot\dfrac{16}{11}\\ =\dfrac{31}{11}\\ b.\dfrac{5-\dfrac{5}{3}+\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}+\dfrac{8}{9}-\dfrac{8}{27}}:\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{16}{121}}\\ =\dfrac{5\left(1-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{27}\right)}{8\left(1-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{27}\right)}:\dfrac{15\cdot\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}{16\cdot\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}\\ =\dfrac{5}{8}:\dfrac{15}{16}\\ =\dfrac{5}{8}\cdot\dfrac{16}{15}\\ =\dfrac{2}{3}\)
\(c.\dfrac{\left(\dfrac{-5}{7}-\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{11}{13}\right)\left(3-\dfrac{3}{4}\right)}{\left(\dfrac{10}{21}+\dfrac{14}{27}-\dfrac{6}{11}+\dfrac{22}{39}\right):\left(2-\dfrac{2}{3}\right)}\\ =\dfrac{-\left(\dfrac{5}{7}+\dfrac{7}{9}-\dfrac{9}{11}+\dfrac{11}{13}\right)\left(3-\dfrac{3}{4}\right)}{\left(\dfrac{10}{21}+\dfrac{14}{27}-\dfrac{12}{22}+\dfrac{22}{39}\right):\dfrac{4}{3}}\\ =\dfrac{-\left(\dfrac{5}{7}+\dfrac{7}{9}-\dfrac{9}{11}+\dfrac{11}{13}\right)\left(3-\dfrac{3}{4}\right)}{\dfrac{2}{3}\left(\dfrac{5}{7}+\dfrac{7}{9}-\dfrac{9}{11}+\dfrac{11}{13}\right)\cdot\dfrac{3}{4}}\\ =\dfrac{-1\cdot\dfrac{9}{4}}{\dfrac{2}{3}\cdot\dfrac{3}{4}}\\ =-\dfrac{9}{4}:\dfrac{2}{4}=-\dfrac{9}{2}\\ d.\dfrac{3+\dfrac{3}{7}-\dfrac{3}{11}+\dfrac{3}{1001}-\dfrac{3}{13}}{\dfrac{9}{1001}-\dfrac{9}{13}+\dfrac{9}{7}-\dfrac{9}{11}+9}\\ =\dfrac{3+\dfrac{3}{7}-\dfrac{3}{11}-\dfrac{3}{13}+\dfrac{3}{1001}}{9+\dfrac{9}{7}-\dfrac{9}{11}-\dfrac{9}{13}+\dfrac{9}{1001}}\\ =\dfrac{3\left(1+\dfrac{1}{7}-\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{1001}\right)}{9\left(1+\dfrac{1}{7}-\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{1001}\right)}\\ =\dfrac{3}{9}=\dfrac{1}{3}\)