Question

\(Thực.hiện.phép.tính:\)

\(\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}...\dfrac{9999}{10000}\)

\(Lưu.ý:Giải.chi.tiết\)

Answer 1

Answer 2

\(\dfrac{3}{4}\cdot\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot...\cdot\dfrac{9999}{10000}\\ =\dfrac{1\cdot3}{2^2}\cdot\dfrac{2\cdot4}{3^2}\cdot\dfrac{3\cdot5}{4^2}\cdot...\cdot\dfrac{99\cdot101}{100^2}\\ =\dfrac{1}{100}\cdot\dfrac{101}{2}\\ =\dfrac{101}{200}\)

Answer 3

3/4 x 8/9 x 15/16 ..x 9999/10000

= 1x3/2x2 x 2x4/3x3 x 3x5/4x4 ..x 99x101/100x100

= 1x2x3x4..x99/2x3x4x5..x100 x 3x4x5x6..x101/2x3x4x5..x100

= 1/100 x 101/2 

= 101/200