Proof of convergence of the series ∑n=1∞(−1)n(1n)

Let the series under consideration be denoted by S; then (1) S=∑n=1∞⁡(−1)n(1n)=1−12+13−14+15−16+… The author of [1] gave a proof of convergence of the series S by noting that (2) (13−14)<(12−13),(1...

Authors

S. C. Dutta Roy (ORCID: https://orcid.org/0000-0002-1723-3850)

Institutions

Indian Institute of Technology Delhi (IN)

Publication Details

Journal: The Mathematical Gazette
Published: 2026-07-01
DOI: https://doi.org/10.1080/00255572.2026.2690533
Primary Topic: Advanced Mathematical Identities
Type: article
Field-Weighted Citation Impact: 0.00

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article

Proof of convergence of the series ∑n=1∞(−1)n(1n)

S. C. Dutta Roy

Jul 1, 2026

The Mathematical Gazette

Advanced Mathematical Identities

article

Proof of convergence of the series ∑n=1∞(−1)n(1n)

S. C. Dutta Roy

July 1, 2026article en

Abstract

The Mathematical Gazette

Indian Institute of Technology Delhi (IN)

Reduced inequalities

Openalex Percentile: Top 3%

Advanced Mathematical Identities

DOI Source OpenAlex

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Proof of convergence of the series ∑n=1∞(−1)n(1n) — S. C. Dutta Roy · The Mathematical Gazette (2026) | TGRS Research Map | TGRS