`Answer:`

\(A=\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}.\frac{48}{49}.\frac{63}{64}\)

\(=\frac{8.15.24.35.48.63}{9.16.25.36.49.64}\)

\(=\frac{2^3.3.5.2^3.3.5.7.2^4.3.3^2.7}{3^2.2^4.5^2.2^2.3^2.7^2.2^6}\)

\(=\frac{3}{2^2}\)

\(=\frac{3}{4}\)

`3/4 xx  8/9 xx 15/16 xx 24/25 xx 35/36`

`= (3xx8xx15xx24xx35)/(4xx9xx16xx25xx36)`

`=(3xx4xx2xx5xx3xx4xx6xx7xx5)/(4xx3xx3xx4xx4xx5xx5xx6xx6)`

`=(2xx7)/(4xx6)`

`=(2xx7)/(2xx2xx6)`

`=7/12`

\(\dfrac{3}{4}\times\dfrac{8}{9}\times\dfrac{15}{16}\times\dfrac{24}{25}\times\dfrac{35}{36}\)

= \(\dfrac{3\times8\times15\times24\times35}{4\times9\times16\times25\times36}\)

= \(\dfrac{3\times\left(2\times4\text{​​}\text{​​}\right)\times\left(3\times5\right)\times\left(6\times4\right)\times\left(5\times7\right)}{4\times\left(3\times3\right)\times\left(4\times4\right)\times\left(5\times5\right)\times\left(6\times6\right)}\)

=\(\dfrac{2\text{​​}\text{​​}\times3\times6\times\left(5\times7\right)}{3\times4\times5\times\left(6\times6\right)}\)

=\(\dfrac{\text{​​}\text{​​}7}{2\times6}\)= \(\dfrac{7}{12}\)

khó vẽ

\(\frac{1\cdot3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\frac{3\cdot5}{4\cdot4}\cdot...\cdot\frac{99\cdot101}{100\cdot100}\)

\(\frac{1\cdot101}{2\cdot100}\)

\(\frac{101}{200}\)

Lời giải:

\(\frac{3}{4}\times \frac{8}{9}\times \frac{15}{16}\times ....\times \frac{99}{100}\)

\(=\frac{3\times 8\times 15\times ....\times 99}{4\times 9\times 16\times ....\times 100}\)

\(=\frac{(1\times 3)\times (2\times 4)\times (3\times 5)\times ...\times (9\times 11)}{2\times 2\times 3\times 3\times 4\times 4\times ....\times 10\times 10}\)

\(=\frac{(1\times 2\times 3\times ...\times 9)\times (3\times 4\times 5\times ....\times 11)}{(2\times 3\times 4\times....\times 10)\times (2\times 3\times 4\times ...\times 10)}\)

\(=\frac{1\times 2\times 3\times ....\times 9}{2\times 3\times 4\times ....\times 10}\times \frac{3\times 4\times 5\times ...\times 11}{2\times 3\times 4\times ...\times 10}\)

\(=\frac{1}{10}\times \frac{11}{2}=\frac{11}{20}\)

\(\dfrac{8}{9}x\dfrac{15}{16}x\dfrac{24}{25}x...\dfrac{8099}{8100}\)

\(=\dfrac{2x4}{3x3}x\dfrac{3x5}{4x4}x\dfrac{4x6}{5x5}x...x\dfrac{89x91}{90x90}\)

\(=\dfrac{2x4x3x5x4x6x...x89x91}{3x3x4x4x5x5x...x90x90}\)

\(=\dfrac{2x91}{3x90}=\dfrac{91}{135}\)

Câu b bạn xem lại đề

Câu 2: 

B = \(\dfrac{25}{21}\) \(\times\) \(\dfrac{49}{45}\) \(\times\) \(\dfrac{81}{77}\) \(\times\)...\(\times\) \(\dfrac{40000}{3999}\)

Các tử số phải là số lẻ nhưng tử số cuối cùng của em lại là số chẵn trái với quy luật. em xem lại đề bài

Đúng ra thì nó phải là: \(\dfrac{39601}{39597}\) chứ không phải là: \(\dfrac{40000}{39999}\)