University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201A Class of Convergent Series with Golden Ratio Based on Fibonacci Sequence1151273432310.22130/scma.2018.62087.231ENMoosaEbadiDepartment of Mathematics, University of Farhangian, Tehran, Iran.FarnazSoltanpourDepartment of Mathematics, University of Farhangian, Tehran, Iran.Journal Article20170417In 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.https://scma.maragheh.ac.ir/article_34323_062ea721f5f1adbe65dd5025387cba8d.pdf