Question

Tìm tổng:

         \(A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{575}\)

Answer 1

\(A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{575}\)

\(\Rightarrow A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{23.25}\)

\(\Rightarrow A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{5}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{23}-\frac{1}{25}\)

\(\Rightarrow A=\frac{1}{3}-\frac{1}{25}\)

\(\Rightarrow A=\frac{25}{75}-\frac{3}{75}\)

\(\Rightarrow A=\frac{22}{75}\)

Answer 2

\(A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{575}\)

   \(=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{23.25}\)

   \(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{23}-\frac{1}{25}\)

   \(=\frac{1}{3}-\frac{1}{25}\)

   \(=\frac{22}{75}\)

Study well ! >_<