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Matrices, Sequences and Sums

  • Alan Camina
  • Barry Lewis
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

This triangle – better described as an array – is associated with the Binomial Theorem  2.1; this expresses the powers of (1+z) in terms of successive powers of z:
$$(1+z)^r=\sum\limits_{k\ge 0}\binom{r}{k}z^k.$$
The next result shows that the coefficients involved represent the number of ways of choosing k elements from r, as assumed in the first chapter.

Keywords

Eulerian Number Fibonacci Number Lower Triangular Matrix Binomial Theorem Lucas Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.School of MathematicsUniversity of East AngliaNorwichUK
  2. 2.The Mathematical AssociationLeicesterUK

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