\(F=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)
\(F=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{30.33}\)
\(F=\frac{1}{3}.\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{30}-\frac{1}{33}\right)\)
\(F=\frac{1}{3}.\left(\frac{1}{3}-\frac{1}{33}\right)\)
\(F=\frac{1}{3}.\frac{10}{33}\)
\(F=\frac{10}{99}\)
\(F=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)
\(=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{30.33}\)
\(=\frac{1}{3}\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{30}-\frac{1}{33}\right)\)
\(=\frac{1}{3}\left(\frac{1}{3}-\frac{1}{33}\right)=\frac{1}{3}\cdot\frac{10}{33}=\frac{10}{99}\)
\(F=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+....+\frac{1}{990}\)
\(F=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+.....+\frac{1}{30.33}\)
\(F=\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+.....+\frac{1}{30}-\frac{1}{33}\)
\(F=\frac{1}{3}-\frac{1}{33}=\frac{11}{33}-\frac{1}{33}=\frac{10}{33}\)
\(F=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+..+\frac{1}{990}\)
\(F=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{30.33}\)
\(F=\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{30}-\frac{1}{33}\)
\(F=\frac{1}{3}-\frac{1}{33}\)
\(F=\frac{11}{33}-\frac{1}{33}\)
\(F=\frac{10}{33}\)
\(F=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)
\(F=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{30.33}\)
\(F=\frac{6-3}{3.6}+\frac{9-6}{6.9}+\frac{12-9}{9.12}+...+\frac{33-30}{30.33}\)
\(3F=\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+....+\frac{1}{30}-\frac{1}{30}-\frac{1}{33}\)
\(3F=\frac{1}{3}-\frac{1}{33}\)
\(F=\left(\frac{1}{3}-\frac{1}{33}\right)\div3\)
\(F=\frac{10}{33}\div3\)
\(F=\frac{10}{99}\)
\(F=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)
\(F=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{30.33}\)
\(F=\frac{1}{3}\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+...+\frac{1}{30}-\frac{1}{33}\right)\)
\(F=\frac{1}{3}\left(\frac{1}{3}-\frac{1}{33}\right)\)
\(F=\frac{1}{3}.\frac{10}{33}\)
\(F=\frac{10}{99}\)
F = \(\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)
= \(\frac{1}{3x6}+\frac{1}{6x9}+\frac{1}{9x12}+...+\frac{1}{30x33}\)
3xF = \(\frac{3}{3x6}+\frac{3}{6x9}+\frac{3}{9x12}+...+\frac{3}{30x33}\)
3xF = \(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{30}-\frac{1}{33}\)
3xF = \(1-\frac{1}{33}=\frac{32}{33}\)
F = \(\frac{32}{33}:3=\frac{32}{99}\)
Ta có : \(F=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+......+\frac{1}{990}\)
\(=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+......+\frac{1}{30.33}\)
\(\Rightarrow3F=\frac{3}{3.6}+\frac{3}{6.9}+\frac{3}{9.12}+......+\frac{3}{30.33}\)
\(\Rightarrow3F=\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+......+\frac{1}{30}-\frac{1}{33}\)
\(\Rightarrow3F=\frac{1}{3}-\frac{1}{33}\)
\(\Rightarrow3F=\frac{10}{33}\)
\(\Rightarrow F=\frac{10}{33}.\frac{1}{3}=\frac{10}{99}\)
