Question

Giải hộ:>

Answer 1

`1. A = (5 . 4^15 . 9^9 - 4 . 3^20 . 8^9)/(5 . 2^10 . 6^19 - 7 . 2^29 . 27^6)`

`= (5 . 2^30 . 3^18 - 2^2 . 3^20 . 2^27)/(5. 2^10 . 2^19 . 3^19 - 7 . 2^29 . 3^18)`

`= (5 . 2^30 . 3^18 - 2^29 . 3^20)/(5 . 2^29 . 3^19  - 7 . 2^29 . 3^18)`

`= (2^29 . 3^18 . (5 . 2 -  3^2))/(2^29 . 3^18 . (5 . 3 - 7))`

`= 1/8`

`2. B = 1/2 . (1+ 1/(1 . 3)).(1+1/(2.4)).(1+1/(3.5)).....(1+1/(2022.2024))`

`= 1/2 . 2^2/1.3 . 3^2/2.4 . 4^2/3.5 ... 2020^2/2019.2021`

`= 1/2 . (2 . 3 . 4 ... 2020)/(1 . 2 . 3 ... 2019) . (2 . 3 . 4 ... 2020)/(3  . 4 . 5 ... 2021)`

`= 1/2 . 2020 . 2/2021`

`= 4040/4042`

`= 2020/2021`