1 − 2 + 4 − 8 + ⋯
In mathematics, 1 − 2 + 4 − 8 + ⋯ is the infinite series whose terms are the successive powers of two with alternating signs. As a geometric series, it is characterized by its first term, 1, and its common ratio, −2. As a series of real numbers it diverges, so in the usual sense it has no sum. In a much broader sense, the series is associated with another value besides ∞, namely 1/3, which is the limit of the series using the 2-adic metric.
1+2+4+8+.1+2+4+8+..1+2+4+8.1+2+4+8..1/2 − 1/4 + 1/8 − 1/16 + ⋯1 + 1 + 1 + 1 + ⋯1 + 2 + 4 + 8 +.1 + 2 + 4 + 8 +..1 + 2 + 4 + 8 +...1 + 2 + 4 + 8 + ⋯1 − 1 + 2 − 6 + 24 − 120 + ...1 − 2 + 3 − 4 + ⋯1 − 2 + 4 − 8 + ...1 − 2 + 4 − 8 + 16 − · · ·1 − 2 + 4 − 8 + · · ·1 − 2 + 4 − 8 + …Divergent geometric seriesGrandi's seriesHistory of Grandi's seriesNegative base
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1 − 2 + 4 − 8 + ⋯
In mathematics, 1 − 2 + 4 − 8 + ⋯ is the infinite series whose terms are the successive powers of two with alternating signs. As a geometric series, it is characterized by its first term, 1, and its common ratio, −2. As a series of real numbers it diverges, so in the usual sense it has no sum. In a much broader sense, the series is associated with another value besides ∞, namely 1/3, which is the limit of the series using the 2-adic metric.
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In matematica, 1 − 2 + 4 − 8 + ...... e dispari: che corrisponde a .
@it
In mathematics, 1 − 2 + 4 − 8 ...... eries using the 2-adic metric.
@en
Szereg 1 − 2 + 4 − 8 + … – sze ...... est skojarzona suma uogólniona
@pl
在數學中,1 − 2 + 4 − 8 + …是一個无穷级数, ...... 它的和不存在。在更广泛的意义下,这一级数有一個廣義的和為⅓。
@zh
数学において、1 − 2 + 4 − 8 + ...は項が連 ...... と広く解釈すると、この級数は一般化された和 1/3 をもつ。
@ja
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In matematica, 1 − 2 + 4 − 8 + ...... e dispari: che corrisponde a .
@it
In mathematics, 1 − 2 + 4 − 8 ...... eries using the 2-adic metric.
@en
Szereg 1 − 2 + 4 − 8 + … – sze ...... est skojarzona suma uogólniona
@pl
在數學中,1 − 2 + 4 − 8 + …是一個无穷级数, ...... 它的和不存在。在更广泛的意义下,这一级数有一個廣義的和為⅓。
@zh
数学において、1 − 2 + 4 − 8 + ...は項が連 ...... と広く解釈すると、この級数は一般化された和 1/3 をもつ。
@ja
label
1 − 2 + 4 − 8 + · · ·
@it
1 − 2 + 4 − 8 + …
@zh
1 − 2 + 4 − 8 + ⋯
@en
1−2+4−8+…
@ja
Szereg 1 − 2 + 4 − 8 + …
@pl