Trả lời:
\(A=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{2499}{2500}\)
\(=\frac{3\cdot8\cdot15\cdot...\cdot2499}{4\cdot9\cdot16\cdot...\cdot2500}\)
\(=\frac{1\cdot3\cdot2\cdot4\cdot3\cdot5\cdot...\cdot49\cdot51}{2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot...\cdot50\cdot50}\)
\(=\frac{\left(1\cdot2\cdot3\cdot...\cdot49\right)\cdot\left(3\cdot4\cdot5\cdot...\cdot51\right)}{\left(2\cdot3\cdot4\cdot...\cdot50\right)\left(2\cdot3\cdot4\cdot...50\right)}\)
\(=\frac{1\cdot51}{50.2}=\frac{51}{100}\)
