Continued fraction with different numerators

Question

In Mathematica, is it possible to form the continued fraction of the following formula? $$ f = a_1+\cfrac{b_1}{a_1+a_2+\cfrac{b_2}{a_2+a_3+\cfrac{b_3}{a_3+a_4+\cfrac{b_4}{a_4+...}}}} $$

@halirutan I read this post before, it's not what I need though. — Tony Dong, Jan 06 '16 at 07:57
Tony, please explain how your situation is different. It looks similar on the surface. — Mr.Wizard, Jan 06 '16 at 07:58
thanks @Mr.Wizard, let me check first, it does look similar~ — Tony Dong, Jan 06 '16 at 08:11

halirutan · Accepted Answer · 2016-01-06T20:43:46.697

5

Well, it is really simple with Fold

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

edited Jan 06 '16 at 20:43

answered Jan 06 '16 at 07:49

halirutan

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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. – Jason B. Jan 06 '16 at 08:20
@JasonB That's what I want. Thanks :) – Tony Dong Jan 06 '16 at 08:25

Continued fraction with different numerators

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