Visualize Geometric Series
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866915682192457728 |
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| author | Chu, Hung Viet |
| author_facet | Chu, Hung Viet |
| contents | We review Mabry's, Edgar's, and the Viewpoints 2000 Group's proofs without words for the geometric series formula. Mabry and Edgar proved without words that
$$\frac{1}{4} + \left(\frac{1}{4}\right)^2 + \left(\frac{1}{4}\right)^3 + \cdots\ =\ \frac{3}{4}\quad\mbox{ and }\quad\frac{4}{9} + \left(\frac{4}{9}\right)^2 + \left(\frac{4}{9}\right)^3 + \cdots\ =\ \frac{4}{5},$$
respectively. We show that their proofs satisfy certain requirements that make them unique. We then illustrate a common idea between their and the Viewpoints 2000 Group's proofs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_05062 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Visualize Geometric Series Chu, Hung Viet History and Overview 40A05 We review Mabry's, Edgar's, and the Viewpoints 2000 Group's proofs without words for the geometric series formula. Mabry and Edgar proved without words that $$\frac{1}{4} + \left(\frac{1}{4}\right)^2 + \left(\frac{1}{4}\right)^3 + \cdots\ =\ \frac{3}{4}\quad\mbox{ and }\quad\frac{4}{9} + \left(\frac{4}{9}\right)^2 + \left(\frac{4}{9}\right)^3 + \cdots\ =\ \frac{4}{5},$$ respectively. We show that their proofs satisfy certain requirements that make them unique. We then illustrate a common idea between their and the Viewpoints 2000 Group's proofs. |
| title | Visualize Geometric Series |
| topic | History and Overview 40A05 |
| url | https://arxiv.org/abs/2006.05062 |