Đáp án:
Giải thích các bước giải:
`1/1.6+1/6.11+1/11.16+...+1/((5n+1).(5n+6))=(n+1)/(5n+6`
`=>5/1.6+5/6.11+5/11.16+...+5/((5n+1).(5n+6))=(5n+5)/(5n+6)`
`=>1-1/6+1/6-1/11+1/11-1/16+...+1/(5n+1)-1/(5n+6)=(5n+5)/(5n+6)`
`=>1-1/(5n+6)=(5n+5)/(5n+6)`
`=>(5n+6-1)/(5n+6)=(5n+5)/(5n+6)`
`=>(5n+5)/(5n+6)=(5n+5)/(5n+6)`
Vậy `1/1.6+1/6.11+1/11.16+...+1/((5n+1).(5n+6))=(n+1)/(5n+6`.
`2`.
`A=1/(1.2.3)+1/(2.3.4)+1/(3.4.5)+...+1/(18.19.20)`
`=>2A=2/(1.2.3)+2/(2.3.4)+2/(3.4.5)+...+2/(18.19.20)`
`=>2A=(3-1)/(1.2.3)+(4-2)/(2.3.4)+(5-3)/(3.4.5)+...+(20-18)/(18.19.20`
`=>2A=1/1.2-1/2.3+1/2.3-1/3.4+1/3.4-1/4.5+...+1/18.19-1/19.20`
`=>2A=1/1.2-1/19.20`
`=>2A=1/2-1/19.20`
`=>A=1/4-1/(2.19.20)<1/4`
`=>A<1/4`
Vậy `A<1/4`.