1 − 2 + 4 − 8 + ⋯
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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.