`1/3 + 1/6 + 1/10 + …+`$\frac{1}{x(x+1):2}$ = `2013/2105`

0 bình luận về “`1/3 + 1/6 + 1/10 + …+`$\frac{1}{x(x+1):2}$ = `2013/2105`”

1. Giải thích các bước giải:

   Ta có:

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

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

   `=>1/6+1/12+1/20+…+1/(x.(x+1))=2013/4030`

   `=>1/2.3+1/3.4+1/4.5+…+1/(x.(x+1))=2013/4030`

   `=>1/2-1/3+1/3-1/4+1/4-1/5+…+1/x-1/(x+1)=2013/4030`

   `=>1/2-1/(x+1)=2013/4030`

   `=>1/(x+1)=1/2-2013/4030=2/4300=1/2015`

   `=>x+1=2015`

   `=>x=2014.`

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2. (giải luôn)

   1/2x(1/3+1/6+….+1/x.(x+1):2=1/2×2013/2105

   1/6+1/12+…+1/x.(x+1)=2013/4030

   1/2.3+1/3,4+…+1/x+1=2013/4030

   1/2-1/x+1=2013/4030

   1/x+1=1/2-2013/4030

   x+1=2015

   x=2014

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