giải giúp em với ạ đang cần gấp lắm :(((

`a ) A = (8-8/5 + 8/25 - 8/125)/(9 - 9/5 + 9/25 - 9/125 )`

`=> A = (8.(1 - 1/5 + 1/25 - 1/125))/(9.(1 - 1/5 + 1/25 - 1/125))`

`=> A = 8/9`

Vì `8/9 = 8/9` nên `A = B`

Vậy `A = B`

`b ) A = (3 + 3/7 - 3/11 + 3/2021 - 3/13)/(9/2021 - 9/13 + 9/7 - 9/11 + 9)`

`=> A = (3.(1 + 1/7 - 1/11 + 1/2021 - 1/13))/(9.(1 + 1/7 - 1/11 + 1/2021 - 1/13 ))`

`=> A = 3/9 = 1/3`

Vì `1/3 < 4/3` nên `A < B`

Vậy `A < B`

`c ) A = 2/(3.7) + 2/(7.11) + 2/(11.15) + ... + 2/(39.43)`

`=> 2A = 4/(3.7) + 4/(7.11) + 4/(11.15) + ... + 4/(39 . 43)`

`=> 2A = 1/3 - 1/7 + 1/7 - 1/11 + 1/11 - 1/15 + ... + 1/39 - 1/43`

`=> 2A = 1/3 - 1/43`

`=> 2A = 40/129`

`=> A = 40/129 : 2`

`=> A = 20/129`

`B = 2/13 = (2.10)/(13.10) = 20/130`

Vì `20/129 > 20/130` nên `A > B`

Vậy `A > B`

`d ) A = 1 + 1/2 + 1/2^2 +  ... + 1/2^2020`

`=> 2A = 2 + 1 + 1/2 + ... + 1/2^2019`

`=> 2A - A = ( 2 + 1 + 1/2 + ... + 1/2^2019 ) - ( 1 + 1/2 + 1/2^2 +  ... + 1/2^2020 )`

`=> A = 2 - 1/2^2020`

Vì `2 - 1/2^2020 < 2` nên `A < B`

Vậy `A < B`

`e ) A = (10^49 + 1)/(10^51 + 1)`

`=> 100A = (100.(10^49 + 1))/(10^51 + 1)`

`=> 100A = (10^51 + 100)/(10^51 + 1)`

`=> 100A = (10^51 + 1 + 99)/(10^51 + 1)`

`=> 100A = 1 + 99/(10^51 + 1)`

`B = (10^48 + 1)/(10^50 + 1)`

`=> 100B = (100.(10^48 + 1))/(10^50 + 1)`

`=> 100B = (10^50 + 100)/(10^50 + 1)`

`=> 100B = (10^50 + 1 + 99)/(10^50 + 1)`

`=> 100B = 1 + 99/(10^50 + 1)`

Vì `9/(10^51 + 1) < 9/(10^50 + 1)` nên `100A < 100B` hay `A < B`

Vậy `A < B`

`#dtkc`