Ta có:\(\frac{8^2}{7.9}.\frac{9^2}{8.10}.\frac{10^2}{9.11}...\frac{14^2}{13.15}=\frac{8^2.9^2.....14^2}{7.9.8.10.9.11....13.15}\)

\(=\)\(\frac{\left(8.9.10...14\right)\left(8.9.10...14\right)}{\left(7.8.9...13\right).\left(9.10.11...15\right)}\)

\(=\frac{14.8}{7.15}=\frac{2.7.8}{7.15}=\frac{2.8}{15}=\frac{16}{15}\)

\(\frac{8^2}{7.9}.\frac{9^2}{8.10}.\frac{10^2}{9.11}.\frac{11^2}{10.12}.\frac{12^2}{11.13}.\frac{13^2}{12.14}.\frac{14^2}{13.15}\)

\(\frac{8^2.9^2.10^2.11^2.12^2.13^2.14^2}{7.9.8.10.9.11.10.12.11.13.12.14.13.15}\)

\(\frac{8.9.10.11.12.13.14}{7.9.10.11.12.13.15}=\frac{8.14}{7.15}=\frac{112}{105}=\frac{16}{15}\)

Học tốt@_@

\(\frac{8^2}{7.9}.\frac{9^2}{8.10}...\frac{14^2}{13.15}\)

\(\frac{8.8}{7.9}.\frac{9.9}{8.10}...\frac{14.14}{13.15}\)

\(\frac{8.9...14}{7.8...13}.\frac{8.9...14}{9.10...15}\)

\(\frac{14}{7}.\frac{8}{15}\)

\(2.\frac{8}{15}\)

\(\frac{16}{15}\)

(8.9.10.11.12.13.14)(8.9.10.11.12.13.14)/7.8.9.10.11.12.13).(9.10.11.12.13.14.15)

=14.8/7.15

=16/15

k cho mình nhá

`A=4/10.12+4/12.14+4/14.16+...+4/96.98`

`=2(2/10.12+2/12.14+2/14.16+...+2/96.98)`

`=2(1/10-1/12+1/12-1/14+1/14-1/16+...+1/96-1/98)`

`=2(1/10-1/98)`

`=2 . 22/245`

`=44/245`

Xem lai.

Đặt \(A=\frac{3}{10.12}+\frac{3}{12.14}+.....+\frac{3}{48.50}\)

      \(A=\frac{3}{2}.\left(\frac{2}{10.12}+\frac{2}{12.14}+......+\frac{2}{48.50}\right)\)

      \(A=\frac{3}{2}.\left(\frac{1}{10}-\frac{1}{12}+....+\frac{1}{48}-\frac{1}{50}\right)\)

       \(A=\frac{3}{2}.\left(\frac{1}{10}-\frac{1}{50}\right)\)

      \(A=\frac{3}{2}.\frac{2}{25}\) 

     \(A=\frac{3}{25}\)

cảm ơn bạn nhiều nhé !