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All these sequences may be viewed as generalizations of the Fibonacci sequence. In particular, Binet's formula may be generalized to any sequence that is a solution of a homogeneous linear difference equation with constant coefficients. Some specific examples that are close, in some sense, to the Fibonacci sequence include:
Excel graph of the difference between two evaluations of the smallest root of a quadratic: direct evaluation using the quadratic formula (accurate at smaller b) and an approximation for widely spaced roots (accurate for larger b). The difference reaches a minimum at the large dots, and round-off causes squiggles in the curves beyond this minimum.
A random Fibonacci sequence can be defined by tossing a coin for each position of the sequence and taking () = + if it lands heads and () = () if it lands tails. Work by Furstenberg and Kesten guarantees that this sequence almost surely grows exponentially at a constant rate: the constant is independent of the coin tosses and was computed in ...
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA).
The Lucas sequence has the same recursive relationship as the Fibonacci sequence, where each term is the sum of the two previous terms, but with different starting values. [1] This produces a sequence where the ratios of successive terms approach the golden ratio, and in fact the terms themselves are roundings of integer powers of the golden ...
Microsoft Office 2019 (second release codenamed Office 16) is a version of Microsoft Office for both Windows and Mac. [9] It was unveiled on April 27, 2018, for Microsoft Windows and June 12, 2018, for macOS , and launched on September 24, 2018. [ 1 ]
The Dottie number is the unique real fixed point of the cosine function. In mathematics, the Dottie number is a constant that is the unique real root of the equation =, where the argument of is in radians. The decimal expansion of the Dottie number is given by: D = 0.739 085 133 215 160 641 655 312 087 673...
An infinite sequence of real numbers (in blue). This sequence is neither increasing, decreasing, convergent, nor Cauchy. It is, however, bounded. In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms).
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