常數的連分數 1

請透過表格求出連分數展開過程中項號 n（≦1000）與結果 fn。

\(\normalsize Continued\ fraction\\ \hspace{50px} f={\large\frac{a_0}{b_0+{\large\frac{a_1}{b_1+{\large\frac{a_2}{b_2+...}}}}}}\\ (1)\ f=\displaystyle \lim_{\small{n \to \infty}}f_n\\ \hspace{50pt}f_n={\large\frac{a_0}{b_0+}\frac{a_1}{b_1+}\frac{a_2}{b_2+}\ \cdots\ \frac{a_n}{b_n+}}\\ (2)\ Example\\ \hspace{30pt} function\hspace{24pt} a_0\hspace{22pt} b_0\hspace{23pt} a_n\hspace{20pt} b_n\\ \hspace{20pt} 1.\hspace{25pt}\pi\hspace{37pt} 4\hspace{26pt} 1\hspace{25pt} n^2\hspace{20pt} 2n+1\\ \hspace{20pt} 2.\hspace{15pt}{\large\frac{1}{e-1}}\hspace{32pt} 1\hspace{28pt} 1\hspace{20pt} n+1\hspace{10pt} n+1\\ \hspace{20pt} 3.\hspace{15pt}\ln\sqrt{2}\hspace{28pt} 1\hspace{28pt} 3\hspace{20pt} -n^2\hspace{10pt} 3(2n+1)\\ \hspace{20pt} 4.\hspace{15pt}\sqrt{2}\hspace{40pt} 2\hspace{28pt} 1\hspace{27pt} 1\hspace{25pt} 2\\ \)