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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 with first term 1 4 and common ratio 1 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.
Prism dioptres. Prism correction is commonly specified in prism dioptres, a unit of angular measurement that is loosely related to the dioptre. Prism dioptres are represented by the Greek symbol delta (Δ) in superscript. A prism of power 1 Δ would produce 1 unit of displacement for an object held 100 units from the prism. [2]
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Heterophoria is the misalignment of the visual axis such that one or both eyes are not properly fixated to an object of interest. When the visual axis is misaligned in such a way, it is corrected by the fusional vergence system. Diagnosis. The cross-cover test, or alternating cover test is usually employed to detect heterophoria.
Esophoria is an eye condition involving inward deviation of the eye, usually due to extra-ocular muscle imbalance. It is a type of heterophoria. Cause. Causes include: Refractive errors; Divergence insufficiency; Convergence excess; this can be due to nerve, muscle, congenital or mechanical anomalies.
Esotropia is a form of strabismus in which one or both eyes turn inward. The condition can be constantly present, or occur intermittently, and can give the affected individual a "cross-eyed" appearance. [1] It is the opposite of exotropia and usually involves more severe axis deviation than esophoria. Esotropia is sometimes erroneously called ...
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, this may be expressed as. The series is related to philosophical questions considered in antiquity, particularly ...