A=1/12+1/20+1/30+1/42+1/56 B=2/15+2/35+2/63+2/99+2/143

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1. $\text{Đáp án + Giải thích các bước giải:}$

   `A=(1)/(12)+(1)/(20)+(1)/(30)+(1)/(42)+(1)/(56)`

   `=>A=(1)/(3.4)+(1)/(4.5)+(1)/(5.6)+(1)/(6.7)+(1)/(7.8)`

   `=>A=(1)/(3)-(1)/(4)+(1)/(4)-(1)/(5)+(1)/(5)-(1)/(6)+(1)/(6)-(1)/(7)+(1)/(7)-(1)/(8)`

   `=>A=(1)/(3)-(1)/(8)`

   `=>A=(5)/(24)`

   `————`

   `B=(2)/(15)+(2)/(35)+(2)/(63)+(2)/(99)+(2)/(143)`

   `=>B=(2)/(3.5)+(2)/(5.7)+(2)/(7.9)+(2)/(9.11)+(2)/(11.13)`

   `=>B=(1)/(3)-(1)/(5)+(1)/(5)-(1)/(7)+(1)/(7)-(1)/(9)+(1)/(9)-(1)/(11)+(1)/(11)-(1)/(13)`

   `=>B=(1)/(3)-(1)/(13)`

   `=>B=(10)/(39)`

    

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2. `A = 1/12 + 1/20 + 1/30 + 1/42 + 1/56`

   `=> A = \frac{1}{ 3.4} + \frac{1}{4.5} + \frac{1}{6.7} + \frac{1}{7.8}`

   `=> A = 1/3 – 1/4 + 1/4 – 1/5 + 1/5 – 1/6 + 1/6 – 1/7 + 1/7 – 1/8`

   `=> A = 1/3 – 1/8`

   `=> A = 5/24`

   `=> B = 2/15 + 2/35 + 2/63 + 2/99 + 2/143`

   `=> B = \frac{2}{3.5} + \frac{2}{5.7} + \frac{2}{7.9} + \frac{2}{9.11} + \frac{1}{11.13}`

   `=> B = 1/3 – 1/5 + 1/5 – 1/7 + 1/7 – 1/9 + 1/9 – 1/11 + 1/11 – 1/13`

   `=> B = 1/3 – 1/13`

   `=> B = 12/39`

    

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