Ta có: \(M=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+\cdots+\frac{1}{990}\)
\(=\frac{1}{3\times6}+\frac{1}{6\times9}+\frac{1}{9\times12}+\cdots+\frac{1}{30\times33}\)
\(=\frac13\times\left(\frac{3}{3\times6}+\frac{3}{6\times9}+\cdots+\frac{3}{30\times33}\right)\)
\(=\frac13\times\left(\frac13-\frac16+\frac16-\frac19+\cdots+\frac{1}{30}-\frac{1}{33}\right)\)
\(=\frac13\times\left(\frac13-\frac{1}{33}\right)=\frac13\times\frac{10}{33}=\frac{10}{99}\)
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