View Proposal #248
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| ID | 248 |
|---|---|
| First Name | Carl |
| Last Name | Cowen |
| Institution | Indiana University--Purdue University Indianapolis |
| Speaker Category | invited |
| Title of Talk | Rearranging the Alternating Harmonic Series |
| Abstract | The commutative property of addition is so familiar to all of us as school children that it comes as a shock to those studying college level mathematics that NOT all 'natural extensions' of the law are true! One of the first instances that we see the failure of an extended commutative law of addition is in infinite series. Often in the introduction to infinite series in calculus, one sees Riemann's Theorem: A conditionally convergent series can be rearranged to sum to any number. Unfortunately, the usual proof of this theorem does not indicate what the sum of a given rearrangement is. In this talk, we will examine the best known conditionally convergent series, the alternating harmonic series, and show how to find the sum of any rearrangement in which the positive terms and the negative terms are each in their usual order. |
| Subject area(s) | |
| Suitable for undergraduates? | ??? |
| Day Preference | |
| Computer Needed? | |
| Bringing a laptop? | Y |
| Overhead Needed? | |
| Software requests | |
| Special Needs | computer projector |
| Date Submitted | 4/8/2008 |
| Year | 2008 |