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GPnotebook is a British medical database for general practitioners (GPs). [1] It is an online encyclopaedia of medicine that provides an immediate reference resource for clinicians worldwide. The database consists of over 30,000 index terms and over two million words of information. GPnotebook is provided online by Oxbridge Solutions Limited.
The geometric series is an infinite series derived from a special type of sequence called a geometric progression.This means that it is the sum of infinitely many terms of geometric progression: starting from the initial term , and the next one being the initial term multiplied by a constant number known as the common ratio .
Diagram illustrating three basic geometric sequences of the pattern 1(r n−1) up to 6 iterations deep.The first block is a unit block and the dashed line represents the infinite sum of the sequence, a number that it will forever approach but never touch: 2, 3/2, and 4/3 respectively.
GP: general practitioner Goodpasture's syndrome: GPA: granulomatosis with polyangiitis: GPCL: gas permeable contact lens: GPT: glutamic-pyruvic transaminase: Gr: grain: GRAV I: gravidity = 1 (indicating a woman during her first pregnancy) GSW: gunshot wound: GTCS: generalised tonic-clonic seizure: GTN: glyceryl trinitrate gestational ...
In trigonometry, the law of tangents or tangent rule [1] is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides. In Figure 1, a , b , and c are the lengths of the three sides of the triangle, and α , β , and γ are the angles opposite those three respective sides.
In general, these series with =, =, =, and = give the expectations of "the number of trials until first success" in Bernoulli processes with "success probability" . The probabilities of each outcome follow a geometric distribution and provide the geometric sequence factors in the terms of the series, while the number of trials per outcome ...
where is the number of terms in the progression and is the common difference between terms. The formula is essentially the same as the formula for the standard deviation of a discrete uniform distribution , interpreting the arithmetic progression as a set of equally probable outcomes.
The cancellation technique, with part of each term cancelling with part of the next term, is known as the method of differences. An early statement of the formula for the sum or partial sums of a telescoping series can be found in a 1644 work by Evangelista Torricelli , De dimensione parabolae .