每日艺题 DAY002
\(a_n\)\(S_n\)联袂数列(有通项) $$ \begin{gather} a_nS_n=\cfrac{1}{4^n},a_1>0,求a_n. \end{gather} $$Attempt1: $$ \begin{gather} 消去S_n:S_n=\cfrac{1}{a_n4^n}\\ S_{n+1}=\cfrac{1}{a_{n+1}4^{n+1}}\\ a_{n+1}=\cfrac{1}{4^{n+1}}({\cfrac{1}{a_{n+1}}-\cfrac{4}{a_n}})\\ =\cfrac{1}{4^{n+1}}({\cfrac{a_{n}-4a_{n+1}}{a_na_{n+1}}}) \end{gather} $$这样的形式还是太复杂了,遂放弃. ...