Worpitzkyʹs Theorem on continued fractions

It is known that under the hypotheses in Worpitzkyʹs Theorem on continued fractions, the approximants converge to the value of the continued fraction with error O(1/n), and that this estimate is best possible. Using a geometric argument we give a more refined estimate of the rate of convergence. We also extend a result of Waadeland that is closely connected to Worpitzkyʹs Theorem.