Question

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F = 1 phần 18 + 1 phần 54 + 1 phần 108 +...+ 1 phần 990

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Answer 1

\(F=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)

\(F=\frac{1}{9}\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)\)

\(F=\frac{1}{9}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)

\(F=\frac{1}{9}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10}-\frac{1}{11}\right)\)

\(F=\frac{1}{9}\left(1-\frac{1}{11}\right)\)

\(F=\frac{1}{9}.\frac{10}{11}=\frac{10}{99}\)