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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 ...
1/4 + 1/16 + 1/64 + 1/256 + ⋯. Archimedes' figure with a = 3 4 . In mathematics, the infinite series 1 4 + 1 16 + 1 64 + 1 256 + ⋯ is an example of one of the first infinite series to be summed in the history of mathematics; it was used by Archimedes circa 250–200 BC. [1] As it is a geometric series ...
The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...
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.
e. The triboelectric effect (also known as triboelectricity, triboelectric charging, triboelectrification, or tribocharging) describes electric charge transfer between two objects when they contact or slide against each other. It can occur with different materials, such as the sole of a shoe on a carpet, or between two pieces of the same material.
Method of image charges. The method of image charges (also known as the method of images and method of mirror charges) is a basic problem-solving tool in electrostatics. The name originates from the replacement of certain elements in the original layout with fictitious charges, which replicates the boundary conditions of the problem (see ...
10 4 ~ 9.65 × 10 4 C: Charge on one mole of electrons (Faraday constant) 10 5: 1.8 × 10 5 C: Automotive battery charge. 50Ah = 1.8 × 10 5 C: 10 6: mega-(MC) 10.72 × 10 6 C: Charge needed to produce 1 kg of aluminium from bauxite in an electrolytic cell: 10 7: 10 8: 5.9 × 10 8 C: Charge in world's largest battery bank (36 MWh), assuming ...
Electron mobility. In solid-state physics, the electron mobility characterises how quickly an electron can move through a metal or semiconductor when pushed or pulled by an electric field. There is an analogous quantity for holes, called hole mobility. The term carrier mobility refers in general to both electron and hole mobility.