1/4 + 1/16 + 1/64 + 1/256 + ⋯
id:
1-4-1-16-1-64-1-256-164-9420275
title:
1/4 + 1/16 + 1/64 + 1/256 + ⋯
text:
In mathematics, the infinite series 1/4 + 1/16 + 1/64 + 1/256 + ⋯ is an example of one of the first infinite series to be summed in the history of mathematics; it was used by Archimedes circa 250–200 BC. As it is a geometric series with first term 1/4 and common ratio 1/4, its sum is ∑ n = 1 ∞ 1 4 n = 1 4 1 − 1 4 = 1 3.
brand slug:
wiki
category slug:
encyclopedia
description:
Infinite sum equal to 1/3 at its limit
original url:
https://en.wikipedia.org/wiki/1/4_%2B_1/16_%2B_1/64_%2B_1/256_%2B_%E2%8B%AF
date created:
2007-03-15T19:08:22Z
date modified:
2024-08-29T01:46:25Z
main entity:
{"identifier":"Q1074845","url":"https://www.wikidata.org/entity/Q1074845"}
image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/a/a0/Geometric_series_14_ell.png","width":578,"height":578}
fields total:
13
integrity:
16