1 − 2 + 4 − 8 + ⋯ a convergent geometric series whose sum is by the usual formula. The Borel sum of is also ; when Émile Borel introduced the limit formulation of Borel summation in 1896, this was one of his first examples after 1 − 1 + 1 − 1 + ⋯ 1 − 2 + 4 − 8 + ⋯ In mathematics, 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
1/2 + 1/4 + 1/8 + 1/16 + ⋯ meters, and so on Zeno argued that the tortoise would always remain ahead of Achilles. The parts of the Eye of Horus were once thought to represent the first six summands of the series. 1/2 + 1/4 + 1/8 + 1/16 + ⋯ In mathematics, the infinite series is an elementary example of a geometric series that converges absolutely. There are many different expressions that can be shown to be equivalent to the problem, such as the form: 2 + 2 + 2 + ... The sum of this series can be denoted in summation notation as: As with any