Đáp án:
`S4=13/79`
`S5=75/61`
`S6=14/19`
Giải thích các bước giải:
* câu S5 sai quy luật nên mk sửa lại ở tử 2 thành 5
`S4=1/1.7+1/7.13+1/13.19+...+1/73.79`
`=1/6[1-1/7+1/7-1/13+1/13-1/19+...+1/73-1/79]`
`=1/6[1-(1/7-1/7+1/13-1/13+...-1/73+1/79)]`
`=1/6[1-1/79]`
`=1/6*78/79`
`=13/79`
`S5=5/2.4+5/4.6+...+5/120.122`
`=5/2[1/2-1/4+1/4-1/6+...+1/120-1/122]`
`=5/2[1/2-(1/4-1/4+1/6-...-1/120+1/122)]`
`=5/2[1/2-1/122]`
`=5/2*30/61`
`=75/61`
`S6=3/1.5+3/5.9+...+3/53.57`
`=3/4[1-1/5+1/5-1/9+...+1/53-1/57]`
`=3/4[1-(1/5-1/5+1/9-1/9+...+1/53-1/53+1/57)]`
`=3/4[1-1/57]`
`=3/4*56/57`
`=14/19`