`S=` $\frac{1}{1.2.3}+$ $\frac{1}{2.3.4}+$ $\frac{1}{3.4.5}+…+$ $\frac{1}{2017.2018.2019}$

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1. Đáp án:

   `⇒S=\frac{1018585}{4074342}`

   Giải thích các bước giải:

    `S=\frac{1}{1.2.3}+\frac{1}{2.3.4}+….+\frac{1}{2017.2018.2019}`

   `⇒S=\frac{1}{2}.(\frac{2}{1.2.3}+\frac{2}{2.3.4}+….+\frac{2}{2017.2018.2019})`

   `⇒S=\frac{1}{2}.(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+….+\frac{1}{2017.2018}-\frac{1}{2018.2019})`

   `⇒S=\frac{1}{2}.(\frac{1}{2}-\frac{1}{4074342})`

   `⇒S=\frac{1018585}{4074342}`

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2. `S = 1/(1.2.3) + 1/(2.3.4) + 1/(3.4.5) + … + 1/(2017 . 2018 . 2019)`

   `2S = 2 . (1/(1.2.3) + 1/(2.3.4) + 1/(3.4.5) + … + 1/(2017 . 2018 . 2019))`

   `2S = 2/(1.2.3) + 2/(2.3.4) + 2/(3.4.5) + … + 2/(2017 . 2018 . 2019)`

   `2S = 1/(1.2) – 1/(2.3) + 1/(2.3) + 1/(3.4) + … + 1/(2017 . 2018) – 1/(2018 . 2019)`

   `2S = 1/(1.2) – 1/(2018 . 2019)`

   `2S = 1/2 – 1/4074342`

   `2S = 2037170/4074342`

   `S = 1018585/4074342`

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