- #1
psychohistory
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Howdy!
Question - What is the value of the continued fraction: 1 + 1/(2 + 1/(3 + 1/(4 + ...
The continued fraction can also be written: [1; 2,3,4,...]
Is there a general method for solving continued fractions with patterns like this? I tried using the recursive formula for the nth convergent, but I couldn't generalize it.
I know how to work with periodic continued fractions (in which case, the value is a quadratic surd), but anything beyond that and I'm clueless.
First post, btw. I'm actually a music major that dabbles in this crap on the side. Thanks!
Question - What is the value of the continued fraction: 1 + 1/(2 + 1/(3 + 1/(4 + ...
The continued fraction can also be written: [1; 2,3,4,...]
Is there a general method for solving continued fractions with patterns like this? I tried using the recursive formula for the nth convergent, but I couldn't generalize it.
I know how to work with periodic continued fractions (in which case, the value is a quadratic surd), but anything beyond that and I'm clueless.
First post, btw. I'm actually a music major that dabbles in this crap on the side. Thanks!