Đáp án:
Em xem lại đề nhé : phải là `B/A` nhé
Xét `A = 1/(1 . 2) + 1/(3 . 4) + ... + 1/(99 . 100)`
`⇔ A = 1 - 1/2 + 1/3 - 1/4 + ... + 1/99 - 1/100`
`⇔ A = (1 + 1/2 + 1/3 + 1/4 + ... + 1/99 + 1/100) - 2 . (1/2 + 1/4 + ... + 1/100)`
`⇔ A = 1/51 + 1/51 + .... + 1/100`
Xét `B = 2017/51 + 2017/52 + ... + 2017/100`
`⇔ B = 2017 . (1/51 + 1/52 + ... + 1/100)`
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`⇔ B/A = (2017 . (1/51 + 1/52 + ... + 1/100))/(1/51 + 1/51 + .... + 1/100)`
`⇔ B/A = 2017`
`⇔ đpcm`