`1/90 – 1/72 – 1/56 – 1/42 -1/30-…-1/2`

Question

`1/90 – 1/72 – 1/56 – 1/42 -1/30-…-1/2`

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Eva 2 tuần 2021-09-08T14:17:35+00:00 2 Answers 7 views 0

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    0
    2021-09-08T14:18:44+00:00

    `1/(90)-1/(72)-1/(56)-1/(42)-1/(30)-1/(20)-1/(12)-1/6-1/2`

    `=1/(90)-(1/(72)+1/(56)+1/(42)+1/(30)+1/(20)+1/(12)+1/6+1/2)`

    `=1/(90)-(1/(1.2)+1/(2.3)+1/(3.4)+1/(4.5)+1/(5.6)+1/(6.7)+1/(7.8)+1/(8.9))`

    `=1/(90)-(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/(90)-(1-1/9)`

    `=1/(90)-8/9`

    `=-79/90`

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    0
    2021-09-08T14:19:05+00:00

    Đáp án:

     

    Giải thích các bước giải:

    `1/90 -1/72-1/56 -1/42-1/30 -…-1/2`

    `=2/90 -(1/90+1/72+1/56 +1/42+1/30 +…+1/2)`

    `=1/45 -(1/(1.2) +1/(2.3) +…+1/(5.6) +1/(6.7)+1/(7.8)+1/(8.9)+1/(9.10))`

    `=1/45-(1-1/2+1/2-1/3+…+1/8-1/9+1/9-1/10)`

    `=1/45 -(1- 1/10)`

    `=1/45 -9/10`

    `=(-79)/90`

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