Đáp án:
`10/11`
Giải thích các bước giải:
Cách 1 :
`1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110`
`= 1/(1xx2) + 1/(2xx3) + 1/(3xx4) + 1/(4xx5) + 1/(5xx6) + 1/(6xx7) + 1/(7xx8) + 1/(8xx9) + 1/(9xx10) + 1/(10xx11)`
`= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + 1/8 - 1/10 + 1/10 - 1/11`
`= 1 - 1/11`
`= 11/11 - 1/11`
`= 10/11`
Cách 2 : Quy đồng
`1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110`
`= 13860/27720 + 4620/27720 + 2310/27720 + 1386/27720 + 924/27720 + 660/27720 + 495/27720 + 385/27720 + 308/27720 + 252/27720`
`= 25200/27720`
`= (2520xx10)/(27720xx11)`
`= 10/11`