Rút gọn biểu thức Cảm ơn mọi người

Đáp án:

9) `3/20`

10) `9/8`

11) `-79/90`

12) `0`

Giải thích các bước giải:

9) `1/10 + 1/40 + 1/88 + 1/154 + 1/238 + 1/340`

`= 1/2.5 + 1/5.8 + 1/8.11 + 1/11.14 + 1/14.17 + 1/17.20`

`= 1/3 (3/2.5 +  3/5.8 + 3/8.11 + 3/11.14 + 3/14.17 + 3/17.20)`

`= 1/3 (1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + 1/11 - 1/14 + 1/14 - 1/17 + 1/17 - 1/20)`

`= 1/3 (1/2 - 1/20)`

`= 1/6 - 1/60 = 3/20`

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10) `3/1.2 - 5/2.3 + 7/3.4 - 9/4.5 + 11/5.6 - 13/6.7 + 15/7.8`

`= (1 - 1 + 1/2 - 1/2 + 1/3 - 1/3 + 1/4) + (1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8)`

`= 1/4 + (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +....+ 1/7 - 1/8)`

`= 1/4 + (1 - 1/8)`

`= 1/4 + 7/8 = 2/8 + 7/8 = 9/8`

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11) `1/9.10 - 1/8.9 - 1/7.8 -...- 1/1.2`

`= - (1/1.2 +....+ 1/7.8 + 1/8.9) + 1/9.10`

`= - (1 - 1/2 +....+ 1/7 - 1/8 + 1/8 - 1/9) + 1/90`

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

`= - 8/9 + 1/90 = -79/90`

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12) `8/9 - 1/72 - 1/56 - 1/42 - 1/30 - 1/20 - 1/12 - 1/6 - 1/2`

`= 8/9 - (1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72)`

`= 8/9 - (1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9)`

`= 8/9 - (1 - 1/2 + 1/2 - 1/3 +...+ 1/7 - 1/8 + 1/8 - 1/9)`

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

`= 8/9 - 1 + 1/9 = 1-1=0`

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