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

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1. 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`

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2. Đáp án:

   `10/11`

   Giải thích các bước giải:

   `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+1/9-1/10+1/10-1/11`

   `=1-1/11`

   `=10/11`

    

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