Question

Tính nhanh

A=\(\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}....\dfrac{2409}{2500}\)

Answer 1

\(A=\dfrac{3}{4}\cdot\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot...\cdot\dfrac{2409}{2500}\\ =\dfrac{1\cdot3}{2\cdot2}\cdot\dfrac{2\cdot4}{3\cdot3}\cdot\dfrac{3\cdot5}{4\cdot4}\cdot...\cdot\dfrac{49\cdot51}{50\cdot50}\\ =\dfrac{1}{2}\cdot\dfrac{3}{2}\cdot\dfrac{2}{3}\cdot\dfrac{4}{3}\cdot\dfrac{3}{4}\cdot\dfrac{5}{4}\cdot...\cdot\dfrac{49}{50}\cdot\dfrac{51}{50}\\ =\dfrac{1}{2}\cdot1\cdot1\cdot...\cdot1\cdot\dfrac{51}{50}\\ =\dfrac{1}{2}\cdot\dfrac{51}{50}\\ =\dfrac{51}{100}\)