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harmonic series

infinite series of the reciprocals of the positive integers
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Summary

harmonic series is a series diverging to infinity[1]. It draws 3,391 Wikipedia views per month (series diverging to infinity category, ranking #2 of 4).[2]

Key Facts

  • Commons category: Harmonic series (mathematics)[3]
  • Described by source: Great Soviet Encyclopedia (1926–1947)[4], Armenian Soviet Encyclopedia, vol. 6[5], Khan Academy[6]
  • Different from: harmonic series[7], alternating harmonic series[8]
  • Maintained by WikiProject: WikiProject Mathematics[9]

Why It Matters

harmonic series has Wikipedia articles in 26 language editions, a strong signal of global cultural recognition.[10] It is known by 44 alternative names across languages and contexts.[11]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] ↑ . wikidata.org.
  2. [4] ↑ . wikidata.org.
  3. [5] ↑ . wikidata.org.
  4. [6] ↑ . wikidata.org.
  5. [7] ↑ . wikidata.org.
  6. [8] ↑ . wikidata.org.
  7. [9] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [10] ↑ . Wikidata sitelinks. wikidata.org.
  3. [11] ↑ . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). harmonic series. Retrieved October 10, 2026, from https://4ort.xyz/entity/harmonic-series
MLA “harmonic series.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Oct. 2026, https://4ort.xyz/entity/harmonic-series.
BibTeX @misc{4ortxyz_harmonic-series_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{harmonic series}}, year = {2026}, url = {https://4ort.xyz/entity/harmonic-series}, note = {Accessed: 2026-10-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): harmonic series — https://4ort.xyz/entity/harmonic-series (retrieved 2026-10-10)

Canonical URL: https://4ort.xyz/entity/harmonic-series · Last refreshed:

Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 5d ago · AddyLockPool · 2026-10-07 view diff on Wikidata ↗
    Encyclopedia of mathematics article id → Harmonic_series, Harmonic_Series
    Described by source → Great Soviet Encyclopedia (1926–1947), Armenian Soviet Encyclopedia, vol. 6, Khan Academy
    Sitelink count → 49
    Wikipedia languages → ['ar', 'bg', 'bs', 'ca', 'ckb', 'commons', 'cs', 'cv', 'da', 'de', 'en', 'eo', '
    + 1 other property edited (see Wikidata diff for full list)
    "/* wbeditentity-statements-multiple-properties-add:0||2 */ Add 3 sources/identifiers (via Wikidata Source Saver, user-initiated)"
  2. 22w ago · KrBot bot · 2026-05-06 view diff on Wikidata ↗
    Great russian encyclopedia online id (2017) → 2344983
    Maintained by wikiproject → WikiProject Mathematics
    Instance of → series diverging to infinity
    Different from → harmonic series, alternating harmonic series
    + 3 other properties edited (see Wikidata diff for full list)
    "/* wbsetqualifier-update:1| */ Symbol represents: positive integer, разрешение перенаправления / resolving redirect positive integer → positive integer ([[:toollabs:editgroups/b/KrBotResolvingRedirect"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.