Đáp án:
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`a.`
Đặt `A = 1/2 - 1/(2×3) - 1/(3×4) - ... - 1/(98 × 99) - 1/99`
`↔ A = 1/2 - [1/(2×3) + 1/(3×4) + ... + 1/(98 × 99)] - 1/99`
`↔ A = 1/2- [1/2 - 1/3 + 1/3 - 1/4 + ... + 1/98 - 1/99] - 1/99`
`↔ A = 1/2 - [1/2 + (- 1/3 + 1/3 - 1/4 + ... + 1/98) - 1/99] - 1/99`
`↔ A = 1/2 - [1/2 - 1/99] - 1/99`
`↔ A = 1/2 - 1/2 + 1/99 - 1/99`
`↔ A = (1/2 - 1/2) + (1/99 - 1/99)`
`↔ A = 0`
Vậy `A = 0`
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`b,`
Đặt `B = 1/2 - 1/(3×7) - 1/(7 × 11) - ... - 1/(19 × 23) - 1/(23 × 27)`
`↔ B = 1/2 - [1/(3×7) + 1/(7 × 11) + ... + 1/(19 × 23) + 1/(23 × 27)]`
`↔ B = 1/2 - 1/4 × [1/3 - 1/7 + 1/7 - 1/11 + ... + 1/19 - 1/23 + 1/23 - 1/27]`
`↔ B = 1/2 - 1/4 × [1/3 + (- 1/7 + 1/7 - 1/11 + ... + 1/19 - 1/23 + 1/23)- 1/27]`
`↔ B = 1/2 -1/4 × [1/3 - 1/27]`
`↔ B = 1/2 - 1/4 × 8/27`
`↔ B = 1/2 - 2/27`
`↔ B = 23/54`
Vậy `B = 23/54`
