Question

Tính tích

A=\(\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x....x\frac{2499}{2500}\)

Answer 1

A = \(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.......\frac{2499}{2500}\)

A = \(\frac{1.3.2.4.3.5.......49.51}{2.2.3.3.4.4........50.50}\)

A = \(\frac{\left(1.2.3.......49\right).\left(3.4.5.....51\right)}{\left(2.3.4.....50\right)\left(2.3.4.....50\right)}\)

A = \(\frac{51}{50.2}\)

A = \(\frac{51}{100}\)

Answer 2

A = \(\frac{1.3}{2.2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\cdot\cdot\cdot\cdot\frac{49\cdot51}{50\cdot50}=\frac{1\cdot3\cdot2\cdot4\cdot...\cdot49\cdot51}{2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot\cdot\cdot\cdot50\cdot51}=\frac{1\cdot51}{2\cdot50}=\frac{51}{100}\)