Question

Tìm x biết:

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{199.200}+\frac{1}{2}x=1\frac{1}{2}\)

Answer 1

\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{199}-\frac{1}{200}+\frac{1}{2}x=\frac{3}{2}\)

\(\Leftrightarrow1-\frac{1}{200}+\frac{1}{2}x=\frac{3}{2}\)

\(\Leftrightarrow\frac{199}{200}+\frac{1}{2}x=\frac{3}{2}\)

\(\Leftrightarrow\frac{1}{2}x=\frac{3}{2}-\frac{199}{200}\)

\(\Leftrightarrow\frac{1}{2}x=\frac{101}{200}\)

\(\Leftrightarrow x=\frac{101}{200}:\frac{1}{2}\)

\(\Leftrightarrow x=\frac{101}{100}\)

Answer 2

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{199.200}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{199}-\frac{1}{200}=1-\frac{1}{200}=\frac{199}{200}\)

=> \(\frac{199}{200}+\frac{1}{2}x=1\frac{1}{2}=\frac{3}{2}\Rightarrow\frac{1}{2}x=\frac{101}{200}\Rightarrow x=\frac{101}{100}\)

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