Generalization of Fibonacci Numbers with Binomial Coefficients and Figurate Numbers
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.
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