Question

1/2 .x-1/1.2-1/2.3-..........-1/45.46=-2

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Answer 1

\(\frac{1}{2.x}-\frac{1}{1.2}-\frac{1}{2.3}-......-\frac{1}{45.46}=-2\)2

\(\frac{1}{2.x}-\left(\frac{1}{1.2}+\frac{1}{2.3}+.......+\frac{1}{45.46}\right)=-2\)

Đặt \(A=\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{45.46}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{45}-\frac{1}{46}\)

\(A=1-\frac{1}{46}=\frac{45}{46}\)

Ta có: \(\frac{1}{2.x}-\frac{45}{46}=-2\)

\(\frac{1}{2.x}=\frac{-47}{46}\)

\(\frac{-47}{-94.x}=\frac{-47}{46}\)

\(\Rightarrow x=\frac{-23}{47}\)