Generalization of Fibonacci Numbers with Binomial Coefficients and Figurate Numbers

Arka Mehatari

Title:
Generalization of Fibonacci Numbers with Binomial Coefficients and Figurate Numbers

Authors:
Arka Mehatari

Cite This Article :

Arka Mehatari "Generalization of Fibonacci Numbers with Binomial Coefficients and Figurate Numbers" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-5, August 2021, pp.2330-2338, URL: https://www.ijtsrd.com/papers/ijtsrd46301.pdf

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Abstract :
Fibonacci Sequence has formed the groundwork of Mathematicians for research in Number Theory. Fibonacci has a profound influence all around us. There are many interesting identities involving Fibonacci. With the invention of Binet’s Formula (which is the most fundamental formula for finding nth Fibonacci), further search for generalisation of Fibonacci sequence has almost came to an end but it is interesting to know that Fibonacci numbers can be expressed by Binomial Coefficients. Thus, I tried to convey the process of generalisation of Fibonacci using Binomial coefficients.

Keywords :
Introduction and Application of Fibonacci, Fibonacci Numbers from Pascal’s Triangle, Fibonacci Numbers using Binomial Coefficients, Fibonacci Numbers from Figurate Numbers, Some Interesting Sums Involving Fibonacci

Publication Details:

Unique Identification Number : IJTSRD46301

Published In : Volume-5 | Issue-5, August 2021

Page Number(s) : 2330-2338

Publisher Name : IJTSRD | www.ijtsrd.com | E-ISSN 2456-6470

Copyright © 2019 by author(s) and International Journal of Trend in Scientific Research and Development Journal. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/by/4.0)

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