2/3+14/15+34/35+62/63+98/99 Đây là bài tính nhanh ạ

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1. Đáp án:

    `50/11`

   Giải thích các bước giải:

    `2/3 + 14/15 + 34/35 + 62/63 + 98/99`

   `= (1 – 1/3) + (1 – 1/15) + (1 – 1/35) + (1 – 1/63) + (1 – 1/99)`

   `= 1 × 5 – (1/3 + 1/15 + 1/35 + 1/63 + 1/99)`

   `= 5 – (1/3 + 1/15 + 1/35 + 1/63 + 1/99)`

   `= 5 – (2/3 × 1/2 + 2/15 × 1/2 + 2/35 × 1/2 + 2/63 × 1/2 + 2/99 × 1/2)`

   `= 5 – (2/3 + 2/15 + 2/35 + 2/63 + 2/99) × 1/2`

   `= 5 -` $(\dfrac{2}{1 × 3} + \dfrac{2}{3 × 5} + \dfrac{2}{5 × 7} + \dfrac{2}{7 × 9} + \dfrac{2}{9 × 11})$ `× 1/2`

   `= 5 – (1 – 1/3 + 1/3 – 1/5 + 1/5 – 1/7 + 1/7 – 1/9 + 1/9 – 1/11) × 1/2`

   `= 5 – (1 – 1/11) × 1/2`

   `= 5 – 10/11 × 1/2`

   `= 5 – 5/11`

   `= 50/11`

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