TY - JOUR ID - 34323 TI - A Class of Convergent Series with Golden Ratio Based on Fibonacci Sequence JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Ebadi, Moosa AU - Soltanpour, Farnaz AD - Department of Mathematics, University of Farhangian, Tehran, Iran. Y1 - 2019 PY - 2019 VL - 13 IS - 1 SP - 115 EP - 127 KW - Fibonacci numbers KW - Golden Ratio KW - Convergence analysis DO - 10.22130/scma.2018.62087.231 N2 - 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. UR - https://scma.maragheh.ac.ir/article_34323.html L1 - https://scma.maragheh.ac.ir/article_34323_062ea721f5f1adbe65dd5025387cba8d.pdf ER -