Journal ArticleDOI
Classroom note: M-bonacci numbers and their finite sums
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In this paper, two new summation formulas for M-bonacci numbers are given, which are generalizations of the two summation formula for Fibonacci numbers, and the formulas are shown to be equivalent to the two formulas for the M-Bonacci numbers.Abstract:
The note considers M-bonacci numbers, which are a generalization of Fibonacci numbers. Two new summation formulas for M-bonacci numbers are given. The formulas are generalizations of the two summation formulas for Fibonacci numbers.read more
Citations
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Journal ArticleDOI
Sequences with M-bonacci property and their finite sums
TL;DR: In this article, two summation formulas for sequences with M-bonacci property were derived and applied to the arithmetic series, mth g − gonal numbers and the Fibonacci series.
Journal ArticleDOI
Undergraduate Research in Mathematics as a Curricular Option
D.A. Brown,Osman Yürekli +1 more
TL;DR: In this paper, a model is outlined for integrating research activities with undergraduates within the mathematics curriculum, and a sequence of courses designed to engage students in research projects has brought about a change in the mathematical culture of students.
Journal ArticleDOI
Infinite sums of M-bonacci numbers
TL;DR: In this paper, the authors constructed infinite series using M-bonacci numbers in a manner similar to that used in previous studies and investigated the convergence of the series to an integer.
Journal ArticleDOI
M-Bonomial Coefficients and Their Identities.
TL;DR: In this article, the M-bonacci binomial coefficients were introduced, which are similar to the binomial and the Fibonomial coefficients and can be displayed in a triangle similar to Pascal's triangle from which some identities become obvious.
Book ChapterDOI
On m-Bonacci-Sum Graphs
TL;DR: The notion of m-bonacci-sum graphs denoted by \(G_{m,n}\) for positive integers m, n are introduced and it is shown that this graph is bipartite and for \(n\ge 2^{m-2}\), \(\{1,2,\ldots ,n\) has exactly \((m-1)\) components.
References
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Journal ArticleDOI
Fibonacci numbers—finite and infinite series
TL;DR: In this article, various approaches to determining the sum of finite and infinite series with Fibonacci numbers are considered. But the main focus of this paper is on finite series and not infinite series.
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