Dấu "." là dấu nhân bạn nhé.
Ta có:
\(A=1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+...+\dfrac{1}{729.3}\)
\(\Rightarrow3A=3+1+\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{729}\)
\(\Rightarrow3A-A=3-\dfrac{1}{729.3}\)
\(\Rightarrow2A=3-\dfrac{1}{729.3}\)
\(\Rightarrow A=\dfrac{1}{2}\left(3-\dfrac{1}{729.3}\right)\)