RIITESH’S SERIES: MATHEMATICAL ANALYSIS AND ITS VALIDATION USING THE GOLDEN RATIO: A MATHEMATICAL AND PHILOSOPHICAL PERSPECTIVE

Abstract [English]

This paper is introducing Riitesh’s Series which is a novel numerical sequence derived from the sequence of terms by adding the preceding two terms and an additional modification by incorporating the integer function of position of next number by 3. While bearing superficial resemblance to the Fibonacci sequence, the Riitesh’s Series exhibits a faster, multidimensional growth pattern. The paper explores the mathematical foundation, convergence properties, and long-term behavior of the Riitesh’s Series. It also demonstrates that its growth is governed by the Golden Ratio (φ=1.618). Philosophical insights and practical applications in education, therapy, and pattern design are also explored.