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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 evaluation of incomplete exponential Bell polynomial B n,k (x 1,x 2,...) on the sequence of ones equals a Stirling number of the second kind: {} =, (,, …,). Another explicit formula given in the NIST Handbook of Mathematical Functions is
This last non-simple continued fraction (sequence A110185 in the OEIS), equivalent to = [;,,,,,...], has a quicker convergence rate compared to Euler's continued fraction formula [clarification needed] and is a special case of a general formula for the exponential function:
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 ...
Such a function is called a sequence, and, in this case the element is called the n th element of the sequence. The index notation can also be used for distinguishing some variables called parameters from the "true variables". In fact, parameters are specific variables that are considered as being fixed during the study of a problem.
Proof without words of the arithmetic progression formulas using a rotated copy of the blocks. An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that ...
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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: