Đáp án + Giải thích các bước giải:

`A = 2/1.3 + 2/3.5 + 2/5.7 + ... + 2/2021.2023.`

`A = 1/1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/2021 - 1/2023.`

`A = 1/1 - 1/2023.`

`A = 2023/2023 - 1/2023.`

`A = 2022/2023.`

`=>` Vậy `A = 2022/2023.`

`---`

`B = 1/2.5 + 1/5.8 + 1/8.11 + ...  +1/92.95 + 1/95.98.`

`B = 1/3 * (3/2.5 + 3/5.8 + 3/8.11 + ... + 3/92.95 + 9/95.98)`.

`B = 1/3 * (1/2 - 1/5 + 1/5 - 1/8  + ... + 1/92 - 1/95 + 1/95 - 1/98)`

`B = 1/3 * (1/2 - 1/98)`

`B = 1/3 * (49/98 - 1/98)`

`B = 1/3 * 48/98.`

`B = 16/98 = 8/49.`

`=>` Vậy `B = 8/49.`

`---`

`C = 1/8 + 1/24 + 1/48 + ... + 1/9800.`

`C = 1/2 * (2/2.4 + 2/4.6 + 2/6.8 + ... + 2/98.100.)`

`C = 1/2 * (1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + ... + 1/98 - 1/100)`

`C = 1/2 * (1/2 - 1/100)`

`C = 1/2 * (50/100 - 1/100)`

`C = 1/2 * 49/100.`

`C = 49/200.`

`=>` Vậy `C = 49/200.`

`---`

`D = 2/15 + 2/35 + 2/63 + ... + 2/399.`

`D = 2/3.5 + 2/5.7 + 2/7.9 + ... + 2/19.21.`

`D = 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ... + 1/19 - 1/21`

`D = 1/3 - 1/21.`

`D = 7/21 - 1/21.`

`D = 6/21 = 2/7.`

`=>` Vậy `D = 2/7.`