Question

Rút gon: A= 8/9*15/16*24/25*...*2499/2500

giúp mk với nhé!

Answer 1

\(=\frac{2.4}{3^2}.\frac{3.5}{4^2}....\frac{49.51}{50^2}\)

\(=\frac{2.3....49}{3.4....50}.\frac{4.5....51}{3.4....50}\)

\(=\frac{2}{50}.\frac{17}{1}\)

\(=\frac{17}{25}\)

Answer 2

Ta có : \(A=\frac{8}{9}.\frac{15}{16}.....\frac{2499}{2500}\)

\(A=\frac{8.15.....2499}{9.16.....2500}\)

\(A=\frac{\left(2.4\right).\left(3.5\right).....\left(49.51\right)}{\left(3.3\right).\left(4.4\right).....\left(50.50\right)}\)

\(A=\frac{\left(2.3....49\right).\left(4.5....51\right)}{\left(3.4....50\right).\left(3.4.....50\right)}\)

\(A=\frac{2\left(3.4.....49\right).\left(4.5.....50\right).51}{\left(3.4.....49\right).50.3.\left(4.5.....50\right)}\)

\(A=\frac{2.51}{3.50}\)

\(A=\frac{2.17.3}{3.25.2}\)

\(A=\frac{17}{25}\)