Question

A = \(\dfrac{7}{2}\) + \(\dfrac{7}{6}\) + \(\dfrac{7}{12}\) + \(\dfrac{7}{20}\) +.... + \(\dfrac{7}{90}\)
Em xin cách giải ạ, em cảm ơn><

Answer 1

\(A=\dfrac{7}{2}+\dfrac{7}{6}+\dfrac{7}{12}+\dfrac{7}{20}+...+\dfrac{7}{90}\)

\(A=7x\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{90}\right)\)

\(A=7x\left(\dfrac{1}{1x2}+\dfrac{1}{2x3}+\dfrac{1}{3x4}+\dfrac{1}{4x5}+...+\dfrac{1}{9x10}\right)\)

\(A=7x\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)

\(A=7x\left(1-\dfrac{1}{10}\right)\)

\(A=7x\left(\dfrac{10}{10}-\dfrac{1}{10}\right)\)

\(A=7x\dfrac{9}{10}=\dfrac{63}{10}\)