A note on lower bounds for numerical series
R. \'Alvarez-Nodarse, K. Castillo
TL;DR
This paper clarifies that three theorems from a previous publication are actually straightforward consequences of elementary calculus, highlighting the simplicity of their proofs.
Contribution
It demonstrates that the three theorems in the referenced work are derivable from basic calculus principles, simplifying their understanding.
Findings
The three theorems follow from elementary calculus.
Proofs in the original work are formal but unnecessary.
Simplifies the understanding of the theorems' foundations.
Abstract
This note shows that the three theorems presented in J. Math. Anal. Appl. 556 (2026), 130199, whose proofs, in their present formulation, are purely formal, follow from elementary calculus.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsIterative Methods for Nonlinear Equations · Mathematical functions and polynomials · Numerical Methods and Algorithms