Lê Quốc Trần Anh Coordinator
02/08/2017 at 13:39-
\(\dfrac{8}{9}.\dfrac{15}{16}.\dfrac{24}{25}......\dfrac{2499}{2500}\)
\(=\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}.\dfrac{4.6}{5.5}......\dfrac{49.51}{50.50}\)
\(=\dfrac{2.4.3.5.4.6....49.51}{3.3.4.4.5.5.....50.50}\)
\(=\dfrac{2.4.5.6....51}{3.4.5....50}\)
\(=\dfrac{2.51}{3.50}\)
\(=\dfrac{17}{25}\)
Lê Quốc Trần Anh selected this answer. -
Dao Trong Luan 02/08/2017 at 13:55\(\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot\dfrac{24}{25}\cdot...\cdot\dfrac{2499}{2500}=\dfrac{2\cdot4}{3\cdot3}\cdot\dfrac{3\cdot5}{4\cdot4}\cdot\dfrac{4\cdot6}{5\cdot5}\cdot...\cdot\dfrac{49\cdot51}{50\cdot50}\)
\(=\dfrac{2\cdot4\cdot4\cdot6\cdot6\cdot8\cdot...\cdot3\cdot5\cdot5\cdot7\cdot...\cdot49\cdot51}{3\cdot3\cdot4\cdot4\cdot5\cdot5\cdot...\cdot50\cdot50}=\dfrac{2\cdot51}{3\cdot50}=\dfrac{17}{25}\)