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

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

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

A=\(\frac{1}{30}.\frac{2}{31}=\frac{1}{465}\)

bó tay

51/100

\(A=\dfrac{3}{4}\cdot\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot...\cdot\dfrac{899}{900}\\ =\dfrac{1\cdot3}{2\cdot2}\cdot\dfrac{2\cdot4}{3\cdot3}\cdot\dfrac{3\cdot5}{4\cdot4}\cdot...\cdot\dfrac{29\cdot31}{30\cdot30}\\ =\dfrac{1\cdot2\cdot3\cdot...\cdot29}{2\cdot3\cdot4\cdot...\cdot30}\cdot\dfrac{3\cdot4\cdot5\cdot...\cdot31}{2\cdot3\cdot4\cdot...\cdot30}\\ =\dfrac{1}{30}\cdot\dfrac{31}{2}\\ =\dfrac{31}{60}\)

Vậy ...

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

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

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

\(=\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)

\(A=\frac{1\cdot3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot...\cdot\frac{29\cdot31}{30\cdot30}\)

\(A=\frac{1\cdot2\cdot...\cdot29}{2\cdot3\cdot...\cdot30}\cdot\frac{3\cdot4\cdot...\cdot31}{2\cdot3\cdot...\cdot30}=\frac{1}{30}\cdot\frac{31}{2}=\frac{31}{60}\)

Ta có : \(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{899}{900}\)

          \(A=\frac{3.8.15.....899}{4.9.16.....900}\)

         \(A=\frac{\left(1.3\right).\left(2.4\right).\left(3.5\right).....\left(29.31\right)}{2^2.3^2.4^2.....30^2}\)

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

       \(A=\frac{1.31}{30.2}\)

       \(A=\frac{31}{60}\)

A=3/4.8/9 .15/16.....899/900

A=1.3/2^2 .   2.4 /3^2  .   3.5/4^2 ....... 29.31 / 30^2

A= 1.2.3.....29 / 2.3.4....30   .   3.4.5...31 / 2.3.4....30

A=1/30 . 31/2 

A= 31/60

Nhớ k nha

A=\(\frac{31}{60}\)

A=\(\frac{31}{60}\)