5 Tính nhanh 1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90

0 bình luận về “5 Tính nhanh 1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90”

1. `1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90`

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

   `=(\underbrace{1+1+1+…+1}_{\text{9 số hạng}})-(1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)`

   `=9-(1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9+1/9.10)`

   `=9-(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)`

   `=9-(1-1/10)`

   `=9-9/10`

   `=81/10`

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2. Đáp án:

    

   Giải thích các bước giải:

    `1/2`  `+`  `5/6`  `+11/12` `+` `19/20` `+` `29/30` `+` `41/42` `+` `55/56` `+` `71/72` `+` `89/90`

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

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

   `=` `9` `-` `(1/2` `+1/6` `+1/12` `+1/20` `+1/30` `+` `1/42` `+` `1/56` `+` `1/72` `+` `1/90)`

   `=` `9` `-` `(1-1/2` `+` `1/2` `-` `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)`

   `=` `9` `-` `(1-1/10)`

   `=` `9` `-` `9/10`

   `=` `90/10` `-` `9/10`

   `=` `81/10`

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