What question did this study set out to answer?

The aim is to explore the nature of infinity in relation to divergent series and Ramanujan's findings.

June 11, 20260 citationsOpen Access

On the Non-Discrete Nature of Infinity: An Algebraic Analysis of Ramanujan's Extended Results and Boundary Contradictions

Key Points

The aim is to explore the nature of infinity in relation to divergent series and Ramanujan's findings.
Analyzed divergent series by treating infinity as a discrete variable.
Compared findings with Ramanujan's regularized results for linear and cubic series.
Demonstrated contradictions through a proof by contradiction.
Identified a recurring correction factor of approximately -0.0290103234.
Showed that treating infinity as a discrete counting number leads to negative irrational roots.
Established that this treatment contradicts the principle that sequence indexes must belong to the Natural Numbers.

Abstract

This paper documents an unconventional journey into the behavior of divergent series. Instead of viewing infinity () as a distant, unreachable limit, we treat it as a tangible, discrete variable within standard algebraic progression formulas. By comparing these common equations with Srinivasa Ramanujan’s well-known regularized results for linear and cubic series, we uncover a striking anomaly: a recurring correction factor of -0. 0290103234. This constant suggests a hidden geometric pattern within divergent limits. We ultimately provide a proof by contradiction, showing that treating as a discrete counting number leads to negative irrational roots, which violates the principle that sequence indexes must belong to the Natural Numbers (N). This result was derived by myself during Class 8. I have it both on. tex and. pdf format for easy access.

问 AI

Bookmark

View Full Paper