A short remark on a new Fibonacci-type sequence

A short remark on the result of Jozsef Sandor

It is pointed out that, one of the results in the recently published article, ’On the Iyengar-Madhava Rao-Nanjundiah inequality and it’s hyperbolic version’ [3] by J´ozsef S´andor is logically incorrect and new corrected result with it’s proof is presented.

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 se...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

A New Generalization of Fibonacci Sequence and Extended Binet’s Formula

Consider the Fibonacci sequence {Fn}n=0 with initial conditions F0 = 0, F1 = 1 and recurrence relation Fn = Fn−1 + Fn−2 (n ≥ 2). The Fibonacci sequence has been generalized in many ways, some by preserving the initial conditions, and others by preserving the recurrence relation. In this article, we study a new generalization {qn}, with initial conditions q0 = 0 and q1 = 1, which is generated by...

A New Generalization of Fibonacci Sequence & Extended Binet’s Formula

Consider the Fibonacci sequence {Fn}n=0 having initial conditions F0 = 0, F1 = 1 and recurrence relation Fn = Fn−1 + Fn−2 (n ≥ 2). The Fibonacci sequence has been generalized in many ways, some by preserving the initial conditions, and others by preserving the recurrence relation. In this article, we study a new generalization {qn}, with initial conditions q0 = 0 and q1 = 1 which is generated b...