Proof of ?
Proof of continued fractions axiom.
Let be a continued fraction which could be finite or infinite.
By we denote the -th convergent of the continued fraction, i.e.
How to prove the formula formula:
This formula is stated in the book Olds C.D. Continued fractions (Math.Assoc.Am., Yale, 1963) as a part of Problem 7 on page 26, together with a related formula