Bài 1:Tính nhanh A)1/12+1/20+1/30+….+1/9702 B)1/2.5+1/5.8+1/8.11+….+1/92.95+1/95.98

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1. Đáp án:

    `↓↓↓`

   Giải thích các bước giải:

   `A=1/12+1/20+1/30+…+1/9702`

   `A=1/3.4+1/4.5+1/5.6+…+1/98.99`

   `A=1/3-1/4+1/4-1/5+…+1/98-1/99`

   `A=1/3-(1/4-1/4+1/5-…-1/98+1/99)`

   `A=1/3-1/99`

   `A=32/99`

                 ————

   `B=1/2.5+1/5.8+1/8.11+….+1/92.95+1/95.98`

   `B=1/3[1/2-(1/5-1/5+1/8-1/8+1/11-…-1/95+1/98)]`

   `B=1/3(1/2-1/98)`

   `B=1/3×24/49`

   `B=8/49`

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2. a)`1/12`+`1/20`+`1/30`+…+`1/9702`
   =`1/3.4`+`1/4.5`+`1/5.6`+…+`1/98.99`
   =`1/3`-`1/4`+`1/4`-`1/5`+`1/5`-`1/6`+…+`1/98`-`1/99`
   =`1/3`-`1/99`
   =`33/99`-`1/99`
   =`32/99`

   b)`1/2.5+1/5.8+1/8.11+….+1/92.95+1/95.98`
   =`1/3(3/2.5+3/5.8+3/8.11+….+3/92.95+1/95.98)`
   =`1/3(1/2-1/5+1/5-1/8+1/8-1/11+…+1/92-1/95+1/95-1/98)`
   =`1/3(1/2-1/98)`
   =`1/3(49/98-1/98)`
   =`1/3. 24/49`
   =`24/3.49`
   =`8/49`

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