In this paper, authors construct a new type of sequence which is named an extra-super increasing sequence, and give the definitions of the minimal super increasing sequence {a[0], ..., a[l]} and minimal extra-super increasing sequence {z[0], ...,[z]l}. Discover that there always exists a fit n which makes (z[n] / z[n-1] - a[n] / a[n-1])= PHI, where PHI is the golden ratio conjugate with a finite precision able to be expressed by computers. Further, derive the formula radic(5) = 2(z[n] / z[n-1] - a[n] / a[n-1]) + 1, where n corresponds to the demanded precision. Experiments demonstrate that the approach to radic(5) through a term ratio difference is more smooth and expeditious than through a Taylor power series, and convince the authors that lim{n to infinity} (z[n] / z[n-1] - a[n] / a[n-1]) = PHI holds.
翻译:在本文中,作者构建了新型序列,称为超超增序,并给出了最小超增序 {a[0],...,[l]}和最小超增序 {z[0],...,[z]}。发现始终存在一个匹配的 n,使 (z[n] /z[n-1] - a[n-1] / a[n-1] = PHI (PHI),其中PHI 是一个金比方,具有一定精度,计算机可以表达的金比方。此外,还得出公式 Radic (5) = 2(z[n] / z[n-1] - a[n] / a[n-1]) + 1,其中n = 要求的精确。实验表明,通过定期比差比Taylor的电量序列更加平滑和快捷,并使作者相信,光 {n[n-1] - a[n] /[n-1]- a[n] /[n-1] = PHI 持有。