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Continued Fraction of Constants 2

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Calculate the continued fraction of constants b0 + a1 / (b1 + a2 / (b2 + ...).
\(\normalsize f=b_0+{\large\frac{a_1}{b_1+{\large\frac{a_2}{b_2+...}}}}\\\)
b0
First term
an
The numerator of the nth term
bn
Denominator of the n term
Determine the term numbers n (≤ 1000) during the expansion of the continued fraction and the result fn in a table.

\(\normalsize Continued\ fraction\\ \hspace{50px} f=b_0+{\large\frac{a_1}{b_1+{\large\frac{a_2}{b_2+...}}}}\\ (1)\ f=\displaystyle \lim_{\small{n \to \infty}}f_n\\ \hspace{50pt}f_n=b_0+{\large\frac{a_1}{b_1+}\frac{a_2}{b_2+}\ \cdots\ \frac{a_n}{b_n+}}\\ (2)\ Example\\ \hspace{30pt} function\hspace{25pt} b_0\hspace{25pt} a_n\hspace{25pt} b_n\\ \hspace{20pt} 1.\hspace{30pt}\sqrt{2}\hspace{25pt} 1\hspace{30pt} 1\hspace{30pt} 2\\ \hspace{20pt} 2.\hspace{5pt}\phi={\large\frac{\sqrt{5}+1}{2}}\hspace{18pt} 1\hspace{30pt} 1\hspace{30pt} 1\hspace{10pt} {golden\\\ ratio}\\ \hspace{20pt} 3.\hspace{5pt}\phi={\large\frac{\sqrt{5}+1}{2}}\hspace{18pt} 2\hspace{20pt} (-1)^n\hspace{22pt} 2\\\)

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