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1/2 − 1/4 + 1/8 − 1/16 + ⋯ — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/1/2_%E2%88%92_1/4_%2B_1/8_%E2%88%92_1/16_%2B_%E2%8B%AF
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T11:31:00.970Z
SHA-256 of the archived text: d962f5197e330ee46888b1c0fd281133f99eea512d525ffd3772ed89df41643e
Stable URL of this page: https://metraipolis.com/documento/dc_487ade84bbcc

How to cite

1/2 − 1/4 + 1/8 − 1/16 + ⋯ — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/1/2_%E2%88%92_1/4_%2B_1/8_%E2%88%92_1/16_%2B_%E2%8B%AF (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_487ade84bbcc (Metraipolis archive dc_487ade84bbcc, sha256 d962f5197e330ee46888b1c0fd281133f99eea512d525ffd3772ed89df41643e)

BibTeX

@misc{dc487ade84bbcc,
  title = {1/2 − 1/4 + 1/8 − 1/16 + ⋯ — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/1/2_%E2%88%92_1/4_%2B_1/8_%E2%88%92_1/16_%2B_%E2%8B%AF},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_487ade84bbcc; sha256 d962f5197e330ee46888b1c0fd281133f99eea512d525ffd3772ed89df41643e},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/1/2_%E2%88%92_1/4_%2B_1/8_%E2%88%92_1/16_%2B_%E2%8B%AF. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, the infinite series 1/2 − 1/4 + 1/8 − 1/16 + ⋯ is a simple example of an alternating series that converges absolutely. It is a geometric series whose first term is 1/2 and whose common ratio is −1/2, so its sum is ∑ n = 1 ∞ ( − 1 ) n + 1 2 n = 1 2 − 1 4 + 1 8 − 1 16 + ⋯ = 1 2 1 − ( − 1 2 ) = 1 3 . {\displaystyle \sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{2^{n}}}={\frac {1}{2}}-{\frac {1}{4}}+{\frac {1}{8}}-{\frac {1}{16}}+\cdots ={\frac {\frac {1}{2}}{1-(-{\frac {1}{2}})}}={\frac {1}{3}}.}

Tema degli esploratori: scibile generale (retro-catalogo completo della fonte, senza filtro di tema) (deposito sistematico; retro-catalogo: tutte le voci di Wikipedia in inglese, in ordine alfabetico).
Fonte: Wikipedia in inglese, voce «1/2 − 1/4 + 1/8 − 1/16 + ⋯» — https://en.wikipedia.org/wiki/1/2_%E2%88%92_1/4_%2B_1/8_%E2%88%92_1/16_%2B_%E2%8B%AF
Wikidata Q3817838 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q3817838
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/1/2_%E2%88%92_1/4_%2B_1/8_%E2%88%92_1/16_%2B_%E2%8B%AF?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1251594333, consultata il 2026-10-07T11:17:31.722Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: b68a99349d4175cf4467b702af443b51c0cd255ce8fdfcaab9777f08f8ad23c3