1 + 2 + 4 + 8 + ⋯ that and , but the underlying proofs demand careful thinking about the interpretation of endless sums. It is also possible to view this series as convergent in a number system different from the real numbers, namely, the 2-adic numbers. As a series of 2-adic numbers this series converges to the same sum, −1, as was derived above by analytic continuation. 1 + 2 + 4 + 8 + ⋯ In mathematics, is the infinite series whose terms are the successive powers of two. As a geometric series, it is characterized by its first term, 1, and its common ratio, 2.
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