$\frac{x1}{2.4}$ + $\frac{1}{4.6}$+ $\frac{1}{6.8}$ +…+ $\frac{1}{2016.2018}$

0 bình luận về “$\frac{x1}{2.4}$ + $\frac{1}{4.6}$+ $\frac{1}{6.8}$ +…+ $\frac{1}{2016.2018}$”

1. `\frac{1}{2.4} + \frac{1}{4.6} +\frac{1}{6.8} + … + \frac{1}{2016.2018}`

   `= \frac{1}{2}( \frac{1}{2} – \frac{1}{4} + \frac{1}{4} – \frac{1}{6} + \frac{1}{6} – \frac{1}{8} + … + \frac{1}{2016} – \frac{1}{2018} `

   `= \frac{1}{2}( \frac{1}{2} – \frac{1}{2018} ) `

   `= \frac{1}{2} . \frac{1008}{2018} `

   `= \frac{504}{2018} = \frac{252}{1009}`

     

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2. $\text{Đáp án + Giải thích các bước giải:}$

   `\text{Đặt}` `(1)/(2.4)+(1)/(4.6)+(1)/(6.8)+…+(1)/(2016.2018)=A`

   `\text{Ta có :}`

   `A=(1)/(2.4)+(1)/(4.6)+(1)/(6.8)+…+(1)/(2016.2018)`

   `=>2A=(2)/(2.4)+(2)/(4.6)+(2)/(6.8)+…+(2)/(2016.2018)`

   `=>2A=(1)/(2)-(1)/(4)+(1)/(4)-(1)/(6)+(1)/(6)-(1)/(8)+….+(1)/(2016)-(1)/(2018)`

   `=>2A=(1)/(2)-(1)/(2018)`

   `=>2A=(504)/(1009)`

   `=>A=(252)/(1009)`

   $\text{Vậy}$ `(1)/(2.4)+(1)/(4.6)+(1)/(6.8)+…+(1)/(2016.2018)=(252)/(1009)`

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