bai 1 : Tinh nhanh C = 3/30 + 3/42 + 3/56 + 3/72 + 3/90 + 3/110. D = 3/3*4 + 3/4*5 + …. + 3/98*99 + 3/99*100. H= 1/2 + 5/6 + 11/12 + 19/20 + 29/30 +

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1. `C=3/30 + 3/42 + 3/56 + 3/72 + 3/90 + 3/110`

   `⇒ C = 3 × (1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110)`

   `⇒ C = 3 × (1/(5×6) + 1/(6×7) + 1/(7×8) + 1/(8×9) + 1/(9×10) + 1/(10×11))`

   `⇒ C = 3 × (1/5 – 1/6 + 1/6 – 1/7 + 1/7 – 1/8 + 1/8 – 1/9 + 1/9 – 1/10 + 1/10 – 1/11)`

   `⇒ C = 3 × (1/5 – 1/11)`

   `⇒ C = 3/5 – 3/11`

   `⇒ C = 33/55 – 15/55 = 18/55`

   `D = 3/(3×4) + 3/(4×5) +…+ 3/(98×99) + 3/(99×100)`

   `⇒ D = 3 × (1/(3×4) + 1/(4×5) +…+ 1/(98×99) + 1/(99×100))`

   `⇒ D = 3 × (1/3 – 1/4 + 1/4 – 1/5 +…+ 1/98 – 1/99 + 1/99 – 1/100)`

   `⇒ D = 3 × (1/3 – 1/100)`

   `⇒ D = 1 – 3/100 = 97/100`

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

   `⇒ H = (1 – 1/2) + (1 – 1/6) + (1 – 1/12) + … + (1 – 1/72) + (1 – 1/90)`

   `⇒ H = (1 + 1 +…+ 1 + 1+1) – (1/2 + 1/6 + 1/12 + …+1/72+1/90)`

   `⇒ H = 9 – (1/(1×2)+1/(2×3)+1/(3×4)+…+1/(8×9)+1/(9×10))`

   `⇒ H = 9 – (1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 +…+1/9 – 1/10)`

   `⇒ H = 9 – (1 – 1/10)`

   `⇒ H = 9 – 9/10`

   `⇒ H = 90/10 – 9/10 = 81/10`

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