On the Proof of Pascal’s Identity using Vedic Mathematics

doi.org/10.70228/CBJ2022029

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ABSTRACT

This paper presents the proof of Pascal's Identity using the sutras and methods of Vedic Mathematics. From the construction of the proof and the results of the theorem, corollaries have been set up and fundamental properties have been explained. All these finally exhibit  its fascinating product-the Pascal’s Triangle. The fundamental properties of the Pascal’s Triangle are also elaborated and discussed using the lens of Vedic Mathematics, such as, binomial coefficients of the binomial theorem, and the property called unimodality. This paper is a result of the establishment of the different formulas and algorithms of permutations and combinations that is with and without repetition using the methods and techniques of Vedic Mathematics by C. A. Alova (2022), whose results and formulas could be used and applied in proving what are called the combinatorial identities. One of these combinatorial identities is the Pascal’s Identity, named after the French mathematician, inventor, and theologian Blaise Pascal. This paper features the sutras by one more than the one before (sutra no.1), by one less than the one before (sutra no. 14), at sight or by simple observation (sub-sutra 12), and when the total is the same, it is nought (sutra no.5).

Keywords: Pascal’s Identity, Pascal’s Triangle, Vedic Mathematics, Combinatorics, Number Theory, Binomial Theorem