| dbo:abstract |
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 (en) 수학에서, 무한급수 1/2 - 1/4 + 1/8 - 1/16 + ⋯는 절대수렴하는 교대급수의 예이다. 이는 초항이 1/2이고 공비가 −1/2인 기하급수으로, 합은 다음과 같이 계산된다. (ko) 数学において、無限級数 1/2 − 1/4 + 1/8 − 1/16 + … は絶対収束する交項級数の簡単な例である。 これは初項 1/2、公比 −1/2 の等比数列であり、その和は以下のようになる。 (ja) 在数学中，“1/2 − 1/4 + 1/8 − 1/16 + · · ·”这个无穷级数是绝对收敛的交错级数中的一个较为简单的例子。 因为“1/2 − 1/4 + 1/8 − 1/16 + · · ·”是一个为1/2、公比为−1/2的几何级数，所以将它求和有： (zh) |
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wiki-commons:Special:FilePath/Halfminusquarter.png?width=300 |
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https://archive.org/details/springer_10.1007-978-3-662-10225-1 |
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dbc:Geometric_series |
| rdfs:comment |
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 (en) 수학에서, 무한급수 1/2 - 1/4 + 1/8 - 1/16 + ⋯는 절대수렴하는 교대급수의 예이다. 이는 초항이 1/2이고 공비가 −1/2인 기하급수으로, 합은 다음과 같이 계산된다. (ko) 数学において、無限級数 1/2 − 1/4 + 1/8 − 1/16 + … は絶対収束する交項級数の簡単な例である。 これは初項 1/2、公比 −1/2 の等比数列であり、その和は以下のようになる。 (ja) 在数学中，“1/2 − 1/4 + 1/8 − 1/16 + · · ·”这个无穷级数是绝对收敛的交错级数中的一个较为简单的例子。 因为“1/2 − 1/4 + 1/8 − 1/16 + · · ·”是一个为1/2、公比为−1/2的几何级数，所以将它求和有： (zh) |
| rdfs:label |
1/2 − 1/4 + 1/8 − 1/16 + ⋯ (en) 1/2 − 1/4 + 1/8 − 1/16 + ⋯ (ko) 1/2 − 1/4 + 1/8 − 1/16 + ⋯ (ja) 1/2 − 1/4 + 1/8 − 1/16 + … (zh) |
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