Đáp án:
`3/(9 . 14) + 3/(14 . 19) + ... + 3/( (5n - 1) (5n + 4) ) < 1/15`
`⇔ 3 . [1/(9 . 14) + 1/(14 . 19) + ... + 1/( (5n - 1) (5n + 4) )] < 1/15`
`⇔ 3 . 1/5 . [1/9 - 1/14 + 1/14 - 1/19 + ... + 1/(5n - 1) - 1/(5n + 4)] < 1/15`
`⇔ 3/5 [1/9 + (- 1/14 + 1/14 - 1/19 + ... + 1/(5n - 1) - 1/(5n + 4)] < 1/15`
`⇔ 3/5[1/9 - 1/(5n + 4)] < 1/15`
`⇔ 3/5 . 1/9 - 1/(5n + 4) < 1/15`
`⇔ 1/15 - 1/(5n + 4) < 1/15`
`⇔ 1/(5n + 4) > 1/15 - 1/15`
`-> 1/(5n + 4) > 0`
`-> đpcm`
