Tính: 2/2+2/6+2/12+…+2/90 1/1.2+1/2.3+1/3.4+…+1/9.10

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1. Đáp án + Giải thích các bước giải:

   \(\dfrac{2}{2}\) + \(\dfrac{2}{6}\) + \(\dfrac{2}{12}\) + … + \(\dfrac{2}{90}\)

   = \(\dfrac{2}{1.2}\) + \(\dfrac{2}{2.3}\) + \(\dfrac{2}{3.4}\) + … + \(\dfrac{2}{9.10}\)

   = 2(\(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + … + \(\dfrac{1}{9.10}\))

   = 2(1-\(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) – \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) -\(\dfrac{1}{4}\) + … + \(\dfrac{1}{9}\)-\(\dfrac{1}{10}\))

   = 2(1- \(\dfrac{1}{10}\))

   = 2 . \(\dfrac{9}{10}\)

   = $\frac{9}{5}$ 

   \(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + … + \(\dfrac{1}{9.10}\)

   = 1-\(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) – \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) -\(\dfrac{1}{4}\) + … + \(\dfrac{1}{9}\)-\(\dfrac{1}{10}\)

   = 1- \(\dfrac{1}{10}\)

   = \(\dfrac{9}{10}\)

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2. Giải thích các bước giải:

   `2/2+2/6+2/12+…+2/90`
   `=2(1/2+1/6+1/12+…+1/90)`
   `=2(1/1.2+1/2.3+1/3.4+…+1/9.10)`
   `=2(1-1/2+1/2-1/3+1/3-1/4+…+1/9-1/10)`
   `=2(1-1/10)`
   `=2(10/10-1/10)`
   `=2. 9/10`
   `=9/5`
   `1/1.2+1/2.3+1/3.4+…+1/9.10`
   `=1-1/2+1/2-1/3+1/3-1/4+…+1/9-1/10`
   `=1-1/10`
   `=10/10-1/10`
   `=9/10`

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