# Continued fraction of constant (2) Calculator

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

 $\normal f=b_0+{\large\frac{a_1}{b_1+{\large\frac{a_2}{b_2+...}}}}\\$
b0
 the 1st term
an
 the n-th term numerator
bn
 the n-th term denominator
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal Continued\ fraction\\\hspace{50} f=b_0+{\large\frac{a_1}{b_1+{\large\frac{a_2}{b_2+...}}}}\\[20](1)\ f=\lim_{\small{n \to \infty}}f_n\\\hspace{50pt}f_n=b_0+{\large\frac{a_1}{b_1+}\frac{a_2}{b_2+}\ \cdots\ \frac{a_n}{b_n+}}\\[10](2)\ Example\\[10]\hspace{25pt} function\hspace{23pt} b_0\hspace{25pt} a_n\hspace{25pt} b_n\\\hspace{20pt} 1.\hspace{25pt}\sqrt{2}\hspace{45pt} 1\hspace{30pt} 1\hspace{30pt} 2\\\hspace{20pt} 2.\hspace{5pt}\phi={\large\frac{\sqrt{5}+1}{2}}\hspace{18pt} 1\hspace{30pt} 1\hspace{30pt} 1\hspace{10pt} {golden\\\ ratio}\\\hspace{20pt} 3.\hspace{5pt}\phi={\large\frac{\sqrt{5}+1}{2}}\hspace{18pt} 2\hspace{20pt} (-1)^n\hspace{5pt} 2\\$

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