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Building a continued fraction

6 answers

In Mathematica, is it possible to form the continued fraction of the following formula?

f=a1+b1a1+a2+b2a2+a3+b3a3+a4+b4a4+… f = a_1+\cfrac{b_1}{a_1+a_2+\cfrac{b_2}{a_2+a_3+\cfrac{b_3}{a_3+a_4+\cfrac{b_4}{a_4+…}}}}

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1 Answer

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Well, it is really simple with Fold

Fold[a[#2] + b[#2]/(a[#2] + #1) &, 0, Reverse[Range[6]]]

For the updated question, I think you only have to modify this as Fold[a[#2] + b[#2]/(a[#2] + #1) &, (Range[10]~Join~{0}) // Reverse], I put the 0 in there so it doesn’t have a constant in the terminal fraction.

– JasonB

Jan 6 at 8:20

@JasonB That’s what I want. Thanks 🙂

– Tony Dong

Jan 6 at 8:25