Question

1/3+1/6+1/10...+2/x(x+1)=2005/2007

Answer 1

\(2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2005}{2007}\)

\(2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2005}{2007}\)

\(2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2005}{2007}\)

\(2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2005}{2007}\)

\(\frac{1}{x+1}=\frac{1}{2}-\left(\frac{2005}{2007}:2\right)\)

\(\frac{1}{x+1}=\frac{1}{2007}\)

=>x+1=2007

x=2007-1

x=2006

Vậy x=2006

Answer 2

x=2006

Answer 3

$x=2006$

Answer 4

200 

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