Question

\(A=2-\frac{2^3}{35}-\frac{2}{63}^3-\frac{2}{99}^3-\frac{2}{142}^3-\frac{2}{195}^3-\frac{2}{255}^3-\frac{2}{323}^3\)

Tìm A

giải cả bài nha

Answer 1

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

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

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

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

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

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