LECTURE NOTES IN ANALYSIS (2011)
《LECTURE NOTES IN ANALYSIS (2011)》 · 第 332 页 · Section 7.3「Infinite Continued Fractions」
The rational number $(a_0,a_1,\ldots,a_n)=h_n/k_n=r_n$ is called the $n$th convergent to the infinite continued fraction. In the case of a finite simple continued fraction we similarly call the number $(a_0,a_1,\ldots,a_m)$ the $m$th convergent.