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1/2 + 1/4 + 1/8 + 1/16 + ⋯. First six summands drawn as portions of a square. The geometric series on the real line. In mathematics, the infinite series 1 2 + 1 4 + 1 8 + 1 16 + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. In summation notation ...
In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser 's circle problem, has a solution by an inductive method. The greatest possible number of regions, rG = , giving the sequence 1, 2, 4 ...
1/2 − 1/4 + 1/8 − 1/16 + ⋯. Demonstration that 1 2 − 1 4 + 1 8 − 1 16 + ⋯ = 1 3. 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.
Artificial general intelligence – Human-level or stronger AI for a wide range of tasks. Artificial imagination – Artificial simulation of human imagination. Artificial intelligence art – Machine application of knowledge of human aesthetic expressions. Artificial life – Field of study.
Immunoglobulin G. The water-accessible surface area of an IgG antibody. Immunoglobulin G ( IgG) is a type of antibody. Representing approximately 75% of serum antibodies in humans, IgG is the most common type of antibody found in blood circulation. [ 1] IgG molecules are created and released by plasma B cells.
To illustrate: it can be seen that 16 is a superperfect number as σ(16) = 1 + 2 + 4 + 8 + 16 = 31, and σ(31) = 1 + 31 = 32, thus σ(σ(16)) = 32 = 2 × 16. If n is an even superperfect number, then n must be a power of 2 , 2 k , such that 2 k +1 − 1 is a Mersenne prime .
By 2014, its catalog was more than twice the size of library.nu with 1.2 million records. [6] As of 28 July 2019, [update] Library Genesis claims to have more than 2.4 million non-fiction books, 80 million science magazine articles, 2 million comics files, 2.2 million fiction books, and 0.4 million magazine issues.
In mathematics, 1 + 2 + 4 + 8 + ⋯ 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. As a series of real numbers it diverges to infinity, so the sum of this series is infinity. However, it can be manipulated to yield a number of ...