cứu tui zới ^^ hichic

Đáp án+Giải thích các bước giải:

1) `1/(1.3.7) + 1/(3.7.9) + 1/(7.9.13) + 1/(9.13.15) + 1/(13.15.19)`

`= 1/6 . (6/(1.3.7) + 6/(3.7.9) + 6/(7.9.13) + 6/(9.13.15) + 6/(13.15.19)`

`= 1/6 . ((7-1)/(1.3.7) + (9-3)/(3.7.9) + (13-7)/(7.9.13) + (15-9)/(9.13.15) + (19-13)/(13.15.19)`

`= 1/6 . (7/(1.3.7) - 1/(1.3.7) + 9/(3.7.9) - 3/(3.7.9) + 13/(7.9.13) - 7/(7.9.13) + 15/(9.13.15) - 9/(9.13.15) + 19/(13.15.19) - 13/(13.15.19))`

`= 1/6 . (1/(1.3) - 1/(3.7) + 1/(3.7) - 1/(7.9) + 1/(7.9) - 1/(9.13) + 1/(9.13) - 1/(13.15) + 1/(13.15) - 1/(15.19)`

`= 1/6 . (1/3 - 1/(15.19))`

`= 1/6 . 94/285`

`= 47/855`

2) `1/(2.4.6) + 1/(4.6.8) + ..........+ 1/(96.98.100)`

`= 1/8 . (1/(1.2.3) + 1/(2.3.4) + ........... + 1/(48.49.50))`

`= 1/16 . ((3-1)/(1.2.3) + (4-2)/(2.3.4) + ............... + (50-48)/(48.49.50))`

`= 1/16 . (1/(1.2) - 1/(2.3) + 1/(2.3) - 1/(3.4) +..............+ 1/(48.49) - 1/(49.50))`

`= 1/16 . (1/2 - 1/2450)`

`= 1/16 . 612/1225`

`= 153/4900`