Tìm x: x/2008-1/10-1/15-1/21-……..-1/120=5/8

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1. $\frac{x}{2008}$- $\frac{1}{10}$- $\frac{1}{15}$- $\frac{1}{21}$-…- $\frac{1}{120}$= $\frac{5}{8}$

   <=>$\frac{x}{2008}$- $\frac{2}{20}$- $\frac{2}{30}$- $\frac{2}{42}$-…- $\frac{2}{240}$= $\frac{5}{8}$

   <=>$\frac{x}{2008}$-($\frac{2}{20}$+ $\frac{2}{30}$+ $\frac{2}{42}$+…+ $\frac{2}{240}$)= $\frac{5}{8}$

   <=>$\frac{x}{2008}$-2($\frac{1}{4*5}$+ $\frac{1}{5*6}$+ $\frac{1}{6*7}$+…+ $\frac{1}{15*16}$)=$\frac{5}{8}$

   <=>$\frac{x}{2008}$-2($\frac{1}{4}$- $\frac{1}{5}$+$\frac{1}{5}$ -$\frac{1}{6}$+…..+$\frac{1}{15}$- $\frac{1}{16}$=$\frac{5}{8}$

   =>$\frac{x}{2008}$-2($\frac{1}{4}$-$\frac{1}{16}$)=$\frac{5}{8}$

   <=>$\frac{x}{2008}$-$\frac{3}{8}$=$\frac{5}{8}$

   =>$\frac{x}{2008}$=$\frac{5}{8}$+$\frac{3}{8}$

   =>$\frac{x}{2008}$=1

   =>x=2008

   Vậy x=2008 là giá trị cần tìm

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2. `x/2018 – 1/10 – 1/15 – 1/21 -…- 1/120=5/8`

   `⇒ x/2018 – (1/10 + 1/15 + 1/21 +…+ 1/120) = 5/8`

   `⇒ x/2018 – 2 . (1/20 + 1/30 + 1/42 +…+ 1/240) = 5/8`

   `⇒ x/2018 – 2 . (1/4.5 + 1/5.6 + 1/6.7 +…+ 1/15.16) = 5/8`

   `⇒ x/2018 – 2 . (1/4 – 1/5 + 1/5 – 1/6 + 1/6 – 1/7 +…+ 1/15 – 1/16) = 5/8`

   `⇒ x/2018 – 2 . (1/4 – 1/16) = 5/8`

   `⇒ x/2018 – 1/2 + 1/8 = 5/8`

   `⇒ x/2018 = 5/8 + 1/2 – 1/8`

   `⇒ x/2018 = 1`

   `⇒ x = 2018`

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