A Class of Convergent Series with Golden Ratio Based on Fibonacci Sequence

In this article, a class of convergent series based on Fibonacci sequence is introduced for which there is a golden ratio (i.e. $frac{1+sqrt 5}{2}),$ with respect to convergence analysis. A class of sequences are at first built using two consecutive numbers of Fibonacci sequence and, therefore,  new sequences have been used in order  to introduce a  new class of series. All properties of the sequences and  related series are illustrated in the work by providing the details including sequences formula, related theorems, proofs and convergence analysis of  the series.

Keywords:

Fibonacci numbers , Golden Ratio , Convergence analysis