Using Geometric Series Proofs in A Course

We have used the annotated bibliography of proofs of the geometric series sum in our sophomore math major Foundations of Mathematics course.  

The students compare / contrast three or more proofs.  In particular, they should consider these questions:

Does the proof apply to the finite geometric series or only the infinite series?  

Where does the proof use |r| < 1?  Is there any way to interpret the proof if   r>1? What if   -1<r<0?  

Where is the limit concept implicit in the proof?  In the classic proof, we use the fact that the limit of  r^n as n goes to infinity.  Is this implicit in this proof?  

Which proof is most elegant?  Most understandable?  

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          copyright: Besson and Styer, Villanova University   12/22/2007  

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