Question

tính nhanh tổng sau :9/2*5+9/5*8+9/8*11+...+9/65*68

Answer 1

\(\dfrac{9}{2\cdot5}+\dfrac{9}{5\cdot8}+\dfrac{9}{8\cdot11}+...+\dfrac{9}{65\cdot68}\)

\(=\dfrac{3\cdot3}{2\cdot5}+\dfrac{3\cdot3}{5\cdot8}+\dfrac{3\cdot3}{8\cdot11}+...+\dfrac{3\cdot3}{65\cdot68}\)

\(=3\cdot\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+...+\dfrac{1}{65}-\dfrac{1}{68}\right)\)

\(=3\cdot\left(\dfrac{1}{2}-\dfrac{1}{68}\right)\)

\(=3\cdot\left(\dfrac{34}{68}-\dfrac{1}{68}\right)\)

\(=3\cdot\dfrac{33}{68}\)

\(=\dfrac{99}{68}=4\dfrac{25}{68}\)

\(Chúc\) \(bạn\) \(học\) \(tốt\) .