1/6 + 1/12+ 1/20+ 1/30+…+ 1/x nhân ( x+1)=2011/4026

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1. Đáp án:  `x = 2012`

    

   Giải thích các bước giải:

     `1/6 + 1/12 + 1/20 + 1/30 + … + 1/x.(x + 1) = 2011/4026`

   `1/(2X3) + 1/(3X4) + 1/(4X5) + 1/(5X6) + … + 1/(xX (x + 1)) = 2011/4026`

   `1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + 1/5 – 1/6 + … + 1/x – 1/(x+1) = 2011/4026`

   `1/2 – 1/(x+1) = 2011/4026`

   `1/(x+1) = 1/2 – 2011/4026`

   `1/(x+1) = 2013/4026 – 2011/4026`

   `1/(x+1) = 1/2013`

   `x + 1 = 2013`

   `x = 2013 – 1`

   `x = 2012`

    

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2. Ta có:

   $\dfrac{1}{6}$ $+$ $\dfrac{1}{12}$ $+$ $…$ $+$ $\dfrac{1}{x.( x+1)}$ $=$ $\dfrac{2011}{4026}$

   ⇔ $\dfrac{1}{2.3}$ $+$$\dfrac{1}{3.4}$ $+$ $…$ $+$ $\dfrac{1}{x. (x+1)}$ 

   ⇔ $\dfrac{1}{2}$ $-$ $\dfrac{1}{3}$ $+$ $\dfrac{1}{3}$ $-$ $\dfrac{1}{4}$ $+$ $….$ $\dfrac{1}{x}$ $-$ $\dfrac{1}{x+ 1}$ $=$ $\dfrac{2011}{4026}$

   ⇔ $\dfrac{1}{2}$ $-$ $\dfrac{1}{x+ 1}$ $=$ $\dfrac{2011}{4026}$

   ⇔ $\dfrac{1}{x+1}$ $=$ $\dfrac{1}{2}$ $-$ $\dfrac{2011}{4026}$

   ⇔ $\dfrac{1}{x+1}$ $=$ $\dfrac{2}{4026}$ 

   ⇔ $\dfrac{1}{x+1}$ $=$ $\dfrac{1}{2013}$ 

   ⇔ $x$ $+$ $1$ $=$ $2013$

   ⇔ $x$ $=$ $2013$ $-$ $1$

   ⇔ $x$ $=$ $2012$

   Vậy $x$ $=$ $2012$

   Chúc bạn học tốt!

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