# Continued fraction of constant (1)

## Calculates the continued fraction expansion of constant number with n terms. a0/(b0+a1/(b1+a2/(b2+...

 $\normal f={\large\frac{a_0}{b_0+{\large\frac{a_1}{b_1+{\large\frac{a_2}{b_2+...}}}}}}\\$
a0
 the 1st term numerator
b0
 the 1st term denominator
an
 the n-th term numerator
bn
 the n-th term denominator

n fn

 $\normal Continued\ fraction\\\hspace{50} f={\large\frac{a_0}{b_0+{\large\frac{a_1}{b_1+{\large\frac{a_2}{b_2+...}}}}}}\\[20](1)\ f=\lim_{\small{n \to \infty}}f_n\\\hspace{50pt}f_n={\large\frac{a_0}{b_0+}\frac{a_1}{b_1+}\frac{a_2}{b_2+}\ \cdots\ \frac{a_n}{b_n+}}\\[10](2)\ Example\\[10]\hspace{25pt} function\hspace{10pt} a_0\hspace{20pt} b_0\hspace{25pt} a_n\hspace{25pt} b_n\\\hspace{20pt} 1.\hspace{25pt}\pi\hspace{35pt} 4\hspace{26pt} 1\hspace{25pt} n^2\hspace{20pt} 2n+1\\\hspace{20pt} 2.\hspace{15pt}{\large\frac{1}{e-1}}\hspace{30pt} 1\hspace{28pt} 1\hspace{20pt} n+1\hspace{10pt} n+1\\\hspace{20pt} 3.\hspace{15pt}\ln\sqrt{2}\hspace{28pt} 1\hspace{28pt} 3\hspace{20pt} -n^2\hspace{10pt} 3(2n+1)\\\hspace{20pt} 4.\hspace{15pt}\sqrt{2}\hspace{40pt} 2\hspace{28pt} 1\hspace{30pt} 1\hspace{30pt} 2\\$

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