Question

Answer 1

Answer 2

Ta có: \(A=\dfrac{5}{2\cdot5}+\dfrac{5}{5\cdot8}+\dfrac{5}{8\cdot11}+...+\dfrac{5}{47\cdot50}\)

\(=\dfrac{5}{3}\left(\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{47\cdot50}\right)\)

\(=\dfrac{5}{3}\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+...+\dfrac{1}{47}-\dfrac{1}{50}\right)\)

\(=\dfrac{5}{3}\left(\dfrac{1}{2}-\dfrac{1}{50}\right)\)

\(=\dfrac{5}{3}\cdot\dfrac{12}{25}=\dfrac{60}{75}=\dfrac{4}{5}\)