Question

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tìm x biết

1/3 + 1/6 + 1/10 + .....+ 1/x{x+1} = 2014 /2016

Answer 1

[Lightning Farron]

\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{2014}{2016}\)

\(\Leftrightarrow\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{2014}{2016}\)

\(\Leftrightarrow\dfrac{2}{2\cdot3}+\dfrac{2}{3\cdot4}+\dfrac{2}{4\cdot5}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{2014}{2016}\)

\(\Leftrightarrow\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{1007}{2016}\)

\(\Leftrightarrow\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{1007}{2016}\)

\(\Leftrightarrow\dfrac{1}{2}-\dfrac{1}{x+1}=\dfrac{1007}{2016}\)\(\Leftrightarrow\dfrac{1}{x+1}=\dfrac{1}{2016}\)

\(\Leftrightarrow x+1=2016\Leftrightarrow x=2015\)

Answer 2

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