Pengontruksian Golden Ratio dari Barisan Fibonacci

Abstract

There are several ways to construct golden ratio, one of which is using the Fibonacci sequence. The Fibonacci sequence is a sequence that is formed from the addition of two terms, namely a term with the previous term. The construction process begins by forming a  ratio sequence from the Fibonacci sequence. The process is continued by investigating the convergence of the  sequence, starting from checking the limitations and monotony of the (rn) sequence. The investigation of the convergence of the  sequence is continued by using the Cauchy criteria. The sequence  is shown to be a Cauchy sequence, so  is shown to be a convergent sequence. Because  converges, further investigation is carried out to find out the convergence point of the rn sequence which turns out to be convergent towards golden ratio.