Tính nhanh: B=3/3+3/15+3/35+3/63+3/99+3/143

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1. Đáp án:

    

   Giải thích các bước giải:

   B=3/3+3/15+3/35+3/63+3/99+3/143

   B= 1 + 3/15+3/35+3/63+3/99+3/143

   Đặt A = 3/15+3/35+3/63+3/99+3/143

   B = 1 

   A = 5. (3/15+3/35+3/63+3/99+3/143)

   A = 5/2. (2/15+2/35+2/63+2/99+2/143)

   A = 5/2. ( 2/3,5+2/5,7+2/7,9+2/9,11+2/11,13)

   A = 5/2. ( 1/3 – 1/5 + 1/5 – 1/7 + 1/7 – 1/9 + 1/9 – 1/11 + 1/11 – 1/13)

   A = 5/2. ( 1/3 – 1/13)

   A = 5/2.10/39

   A = 50/78 = 25/39

   Ta có :

   = 1 + 25/39  = 39/39 + 25/39 = 64/39

   Vậy B = 64/39

    

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2. B=3/3+3/15+3/35+3/63+3/99+3/143

   B = 3 × ( 1/3 + 1/15 + 1/35 + 1/63 + 1/99 + 1/143 )

   B = 3 × ( 1/1×3 + 1/3×5 + 1/5×7 + … + 1/11×13 )

   B = 3 × ( 1 – 1/3 + 1/3 – 1/5 + 1/5 – 1/7 + … + 1/11 – 1/13 )

   B = 3 × ( 1 – 1/13)

   B = 3 × 12/13

   B = 36/13

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