\(\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{504}\)
\(=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{21.24}\)
\(=\frac{1}{3}.\left(\frac{3}{3.6}+\frac{3}{6.9}+\frac{3}{9.12}+...+\frac{3}{21.24}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{21}-\frac{1}{24}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{3}-\frac{1}{24}\right)\)
\(=\frac{1}{3}.\frac{7}{24}\)
\(=\frac{7}{72}\)
_Chúc bạn học tốt_
=>\(\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{21.24}\)
=>\(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{21}-\frac{1}{24}\)
=> \(\frac{1}{3}-\frac{1}{24}\)\(=\frac{7}{24}\)
