Tính A

\(A=2\frac{2}{35}^3-\frac{2^3}{63}-\frac{2}{99}^3-\frac{2}{143}^3-\frac{2}{195}^3-\frac{2}{255}^3-\frac{2}{323}^3\)

giải cả bài nha

\(A=2-\left(\frac{2^3}{25}+\frac{2^3}{63}+...+\frac{2^3}{255}+\frac{2^3}{323}\right)\)

\(=2-4.\left(\frac{2}{35}+\frac{2}{63}+...+\frac{2}{255}+\frac{2}{323}\right)\)

\(=2-4.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{15.17}+\frac{2}{17.19}\right)\)

\(=2-4.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}\right)\)

\(=2-4.\left(\frac{1}{5}-\frac{1}{19}\right)\)

\(=2-4.\frac{14}{95}=2-\frac{56}{95}=\frac{134}{95}\)

\(C=\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\)

\(C=\frac{2}{3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\)

\(C=\frac{2}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\)

\(C=\frac{2}{3}+\frac{1}{3}-\frac{1}{13}\)

\(C=1-\frac{1}{13}\)

\(C=\frac{12}{13}\)

\(C=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\)

\(C=\frac{1}{1}-\frac{1}{3}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\)

\(C=\frac{1}{1}-\frac{1}{13}\)

\(C=\frac{12}{13}\)

\(C=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\)

\(C=\left(1-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{7}\right)+...+\left(\frac{1}{11}-\frac{1}{13}\right)\)

\(C=1-\frac{1}{13}\)

\(C=\frac{12}{13}\)

\(A=\frac{2}{3}+\frac{2}{15}+...+\frac{2}{143}\)

\(A=\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{11\cdot13}\)

\(A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\)

\(A=1-\frac{1}{13}=\frac{12}{13}\)

   \(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\)

\(=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\)

\(=1-\frac{1}{13}\)

\(=\frac{12}{13}\)

\(\frac{2}{6}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\)

\(=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\)

\(=1-\frac{1}{13}\)

\(=\frac{12}{13}\)