Advertisement

Recursion

  • Matthias Beck
  • Ross Geoghegan
Chapter
Part of the Undergraduate Texts in Mathematics book series (UTM, volume 0)

Abstract

Before You Get Started. You have most likely seen sums of the form \(\sum\nolimits_{j = 1}^k {j = 1 + 2 + 3 + \cdots + k,}\) or products like \(k! = 1 \cdot 2 \cdot 3 \cdots k.\) In this chapter we will use the idea behind induction to define expressions like these. For example, we can define the sum 1+2+3+ ∙ ∙ ∙ +(k+1) by saying, if you know what 1+2+3+ ∙ ∙ ∙ +k means, add k+1 and the result will be 1+2+3+ ∙ ∙ ∙ +(k+1). Think about how this could be done; for example, how should one define 973685! rigorously, i.e., without using ∙ ∙ ∙ ? Find a formula for 1+2+3+ ∙ ∙ ∙ +k.

Keywords

Base Case Induction Step Fibonacci Number Fibonacci Sequence Binomial Theorem 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Matthias Beck and Ross Geoghegan 2010

Authors and Affiliations

  1. 1.Department of MathematicsSan Francisco State UniversitySan FranciscoUSA
  2. 2.Department of Mathematical SciencesBinghamton University State University of New YorkBinghamtonUSA

Personalised recommendations