A=\(\frac{1\times3}{2\times2}\times\frac{2\times4}{3\times3}\times\frac{3\times5}{4\times4}...\times\frac{29\times31}{30\times30}\)

A=\(\frac{1\times2\times3\times...\times29}{2\times3\times4\times...\times30}\times\frac{3\times4\times5\times...\times31}{2\times3\times4\times...\times30}\)

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

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

Tớ cũng giống Như bạn ấy 

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

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

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

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

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

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

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

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

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

\(=\frac{1.3}{2^2}.\frac{2.4}{3^2}.....\frac{29.31}{30^2}=\frac{1.2....29}{2.3....30}.\frac{3.4....31}{2.3....30}\)

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

Dễ vãi gợi ý nha: 

Tách ra sau đó chia làm 2 nhóm tử và mẫu

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

Vậy ...

\(\dfrac{3}{4}\)\(\dfrac{3}{4}\cdot\dfrac{8}{9}\cdot\dfrac{15}{16}......\dfrac{899}{900}=\dfrac{1.3}{2.2}\cdot\dfrac{2.4}{3.3}\cdot\dfrac{3.5}{4.4}\cdot\dfrac{29.31}{30.30}\)

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

=\(\dfrac{1}{30}\cdot\dfrac{31}{2}=\dfrac{31}{60}\)

BỎ đi 1 \(\dfrac{3}{4}\)ở đầu nha mk đánh nhầm

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

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

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

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

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

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