Question

C=\(\dfrac{3}{15\cdot22}+\dfrac{3}{22\cdot29}+...+\dfrac{3}{85\cdot92}\)

giải lại cho mình hiểu bn ngonhuminh

Answer 1

\(C=\dfrac{3}{15\cdot22}+\dfrac{3}{22\cdot29}+...+\dfrac{3}{85\cdot92}\)

\(=\dfrac{3}{7}\left(\dfrac{7}{15\cdot22}+\dfrac{7}{22\cdot29}+...+\dfrac{7}{85\cdot92}\right)\)

\(=\dfrac{3}{7}\left(\dfrac{1}{15}-\dfrac{1}{22}+\dfrac{1}{22}-\dfrac{1}{29}+...+\dfrac{1}{85}-\dfrac{1}{92}\right)\)

\(=\dfrac{3}{7}\left(\dfrac{1}{15}-\dfrac{1}{92}\right)\)\(=\dfrac{3}{7}\cdot\dfrac{77}{1380}=\dfrac{11}{460}\)