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


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.


Base Case Induction Step Fibonacci Number Fibonacci Sequence Binomial Theorem 
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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

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