1/3+1/6+1/10+….+2/x.(x+1)=2013/2015 find x

0 bình luận về “1/3+1/6+1/10+….+2/x.(x+1)=2013/2015 find x”

1. Đáp án:    x = 2014

    

   Giải thích các bước giải:

      $\frac{1}{3}$ + $\frac{1}{6}$ + $\frac{1}{10}$ + … + $\frac{2}{x(x+1)}$ = $\frac{2013}{2015}$ 

   ⇒ $\frac{2}{6}$ + $\frac{2}{12}$ + $\frac{2}{20}$ + … + $\frac{2}{x(x+1)}$ = $\frac{2013}{2015}$ 

   ⇒ $\frac{2}{2.3}$ + $\frac{2}{3.4}$ + $\frac{2}{4.5}$ + … + $\frac{2}{x(x+1)}$ = $\frac{2013}{2015}$ 

   ⇒ 2 . ($\frac{1}{2.3}$ + $\frac{1}{3.4}$ + $\frac{1}{4.5}$ + … + $\frac{1}{x(x+1)}$) = $\frac{2013}{2015}$ 

   ⇒ 2 . ($\frac{1}{2}$ – $\frac{1}{3}$ + $\frac{1}{3}$ – $\frac{1}{4}$ + … + $\frac{1}{x}$ – $\frac{1}{x + 1}$)  = $\frac{2013}{2015}$

   ⇒ 2 . ($\frac{1}{2}$ – $\frac{1}{x + 1}$) = $\frac{2013}{2015}$

   ⇒  $\frac{1}{2}$ – $\frac{1}{x + 1}$ = $\frac{2013}{2015}$ : 2

   ⇒  $\frac{1}{2}$ – $\frac{1}{x + 1}$ = $\frac{2013}{2015}$ . $\frac{1}{2}$ 

   ⇒  $\frac{1}{2}$ – $\frac{1}{x + 1}$ = $\frac{2013}{4030}$ 

   ⇒   $\frac{1}{x + 1}$ = $\frac{1}{2}$ – $\frac{2013}{4030}$ 

   ⇒   $\frac{1}{x + 1}$ = $\frac{2015}{4030}$ – $\frac{2013}{4030}$

   ⇒   $\frac{1}{x + 1}$ = $\frac{1}{2015}$ 

   ⇒   x + 1 = 2015

   ⇒         x = 2015 – 1

   ⇒         x = 2014

   $Cho mình hay nhất nha$

    

    

   Trả lời

2. 1/3+1/6+1/10+….+2/x.(x+1)=2013/2015

   2/6+2/12+2/20 +….+ 2/x.(x+1) = 2013/2015

   2/2×3+2/3×4+2/4×5 +….+ 2/x.(x+1) = 2013/2015

   1/2×3+1/2×3+1/3×4+1/3×4+1/4×5+1/4×5+….+ 1/x.(x+1) + 1/x.(x+1) = 2013/2015

   1/2 – 1/3 + 1/2 – 1/3 + 1/3 – 1/4 + 1/3 – 1/4 + …. + 1/x – 1/x+1 + 1/x – 1/x+1 = 2013/2015

   1/2 – 1/x+1 + 1/2 – 1/x+1 = 2013/2015

   1 – 2/x+1 = 2013/2015

         2/x+1 = 2/2015

   => x= 2014

   Trả lời