Tính A = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + …………. + 1/ 98.99.100

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1. Đáp án:

    `4949/19800`

   Giải thích các bước giải:

   `A` `=` `1/1` `.` `2.3` `+` `1/2` `.` `3` `.`  `4` `+` `1/3` `.` `4` `.` `5` `+` `…` `+` `1/ 98.99.100`

   `=` `1/2` `-` `1/2.3` `+` `1/2.3` `-` `1/3.4` `+` …. `1/98.99` `-` `1/99.100`

   `=` `1/1.2` `-` `1/99.100` 

   `=` `4949/19800`

   $#Đào$

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2. `A = 1/(1 . 2 . 3) + 1/(2 . 3 . 4) + (1/(3 . 4 . 5) + … + 1/(98 . 99 . 100))`

   `A = 1/2 . 2 . (1/(1 . 2 . 3) + 1/(2 . 3 . 4) + (1/(3 . 4 . 5) + … + 1/(98 . 99 . 100))`

   `A = 1/2 . (2 . 1/(1 . 2 . 3) + 1/(2 . 3 . 4) + (1/(3 . 4 . 5) + … + 1/(98 . 99 . 100))`

   `A = 1/2 . (2/(1 . 2 . 3) + 2/(2 . 3 . 4) + 2/(3 . 4 . 5) + … + 2/(98 . 99 . 100))`

   `A = 1/2 . (1/(1 . 2) – 1/(2 . 3) + 1/(2 . 3) – 1/(3 . 4) + … + 1/(98 . 99) – 1/(99 . 100))`

   `A = 1/2 . (1/(1 . 2) – 1/(99 . 100))`

   `A = 1/2 . (1/2 – 1/(99 . 100))`

   `A = 1/(2 . 2) – 1/(2 . 99 . 100)`

   `A = 1/4 – 1/19800`

   `A = 4949/19800`

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