Tính nhanh 1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110

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`