B=1/1.5+1/5.9+…..+1/2016.2020 C=1/10.12+1/12.14+….+1/998.1000

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1. `B= 1/1.5 + 1/5.9 + … + 1/2016.2020`

   `⇒ B = 1/4 . (4/1.5 + 4/5.9 +…+ 4/2016.2020)`

   `⇒ B = 1/4 . (1 – 1/5 + 1/5 – 1/9 +…+ 1/2016 – 1/2020)`

   `⇒ B = 1/4 . (1 – 1/2020)`

   `⇒ B = 1/4 . 2019/2020 = 2019/8080`

   `C= 1/10.12 + 1/12.14 +…+ 1/998.1000`

   `⇒ C = 1/2 . (2/10.12 + 2/12.14 +…+ 2/998.1000)`

   `⇒ C = 1/2 . (1/10 – 1/12 + 1/12 – 1/14 +…+ 1/998 – 1/1000)`

   `⇒ C = 1/2 . (1/10 – 1/1000)`

   `⇒ C = 1/20 – 1/2000 = 99/2000`

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2. Giải thích các bước giải:

   `B=1/1.5+1/5.9+…..+1/2016.2020`
   `B=1/4 . (4/1.5+1/5.9+…+4/2016.2020)`
   `B=1/4 . (1/1-1/5+1/5-1/9+…+1/2016-1/2020)`
   `B=1/4.(1/1-1/2020)`
   `B=1/4 .(2020/2020-1/2020)`
   `B=1/4.(2019/2020)`
   `B=2019/8080`
   `C=1/10.12+1/12.14+….+1/998.1000`
   `C=1/2.(2/10.12+2/12.14+…+2/998.1000)`
   `C=1/2.(1/10-1/12+1/12-1/14+…+1/998-1/1000)`
   `C=1/2.(1/10-1/1000)`
   `C=1/2 . (100/1000-1/1000)`
   `C=1/2.(99/1000)`
   `C=99/2000`

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