Question

1/3 +1/6+ 1/10 + .......+2/x(x+1 ) = 2016/2018

giúp tôi với 

Answer 1

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2016}{2018}\)

<=>  \(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{1008}{1009}\)

<=>  \(2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{1008}{1009}\)

<=>   \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{x}-\frac{1}{x+1}=\frac{504}{1009}\)

<=>  \(\frac{1}{2}-\frac{1}{x+1}=\frac{504}{1009}\)

<=>  \(\frac{1}{x+1}=\frac{1}{2018}\)

=>  \(x+1=2018\)

<=>  \(x=2017\)

Answer 2

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