Question

Nhanh giùm mình nha mai thi rồi.

A=3/4×8/9×15/16.......×899/900

Answer 1

A = \(\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}....\dfrac{899}{900}\)

= \(\left(\dfrac{1.3}{2.2}\right).\left(\dfrac{2.4}{3.3}\right).\left(\dfrac{3.5}{4.4}\right)...\left(\dfrac{29.31}{30.30}\right)\)

= \(\left[\left(1.2.3...29\right).\left(3.4.5...31\right)\right]:\left[\left(2.3.4...30\right).\left(2.3.4...30\right)\right]\)

= \(\dfrac{1.2.3...29}{2.3.4...30}.\dfrac{3.4.5...31}{2.3.4...30}\)

= \(\dfrac{1}{30}.\dfrac{31}{2}\)

= \(\dfrac{31}{62}\)

Answer 2

A= \(\dfrac{3}{4}\).\(\dfrac{8}{9}\).\(\dfrac{15}{16}\).....\(\dfrac{899}{900}\)

A= \(\dfrac{1.3}{2.2}\).\(\dfrac{2.4}{3.3}\).\(\dfrac{3.5}{4.4}\).....\(\dfrac{29.31}{30.30}\)

A= \(\dfrac{\left(1.2.3....29\right)}{\left(2.3.4....30\right)}\) . \(\dfrac{\left(3.4.5....31\right)}{\left(2.3.4....30\right)}\)

A= \(\dfrac{1.2.3....29}{2.3.4....30}\) . \(\dfrac{3.4.5...31}{2.3.4...30}\)

A= \(\dfrac{1}{30}\) . \(\dfrac{31}{2}\)

A= \(\dfrac{31}{6}\)