Question

1/1x3 + 1/3x5 + ...+ 1/X x ( X + 2)= 19/40

Tìm x

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Answer 1

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Answer 2

\(\frac{1}{1\times3}+\frac{1}{3\times5}+...+\frac{1}{x\times\left(x+2\right)}=\frac{19}{40}\)

\(\frac{1}{2}\left(\frac{2}{1\times3}+\frac{2}{3\times5}+...+\frac{2}{x\times\left(x+2\right)}\right)=\frac{19}{40}\)

\(\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{19}{40}\)

  \(1-\frac{1}{x+2}=\frac{19}{40}\times2\)

  \(\frac{x+1}{x+2}=\frac{19}{20}\Rightarrow x=18\)