Tính A= 1/1.2.3+1/2.3.4+…..+1\198.199.200

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1. `A=1/{1.2.3}+1/{2.3.4}+…+1/{198.199.200}`

   `⇒2A=2/{1.2.3}+2/{2.3.4}+…+2/{198.199.200}`

   `⇒2A=1/1.2-1/2.3+1/2.3-1/3.4+…+1/198.19-1/199.200`

   `⇒2A=1/1.2-1/199.200`

   `⇒2A=1/2-1/39800`

   `⇒2A=19900/39800-1/39800`

   `⇒2A=19899/39800`

   `⇒A=19899/79600`

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2. $A= \dfrac{1}{1.2.3} + \dfrac{1}{2.3.4} + …. + \dfrac{1}{198.199.200}$

   $⇔2A=\dfrac{2}{1.2.3} + \dfrac{2}{2.3.4} + …. + \dfrac{2}{198.199.200}$

   $⇔2A = \dfrac{1}{1.2} – \dfrac{1}{2.3} + \dfrac{1}{2.3} – \dfrac{1}{3.4} + ….. + \dfrac{1}{198.199} – \dfrac{1}{199.200}$

   $⇔ 2A = \dfrac{1}{2} – \dfrac{1}{39800}$

   $⇔ 2A = \dfrac{19899}{39800}$

   $⇔ A = \dfrac{19899}{79600}$

    

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