This paper investigates four important methods of solving summation and product problems in mathematics competitions. Chapter 1 presents the basic concepts of sequence and series, including arithmetic sequence (series), geometric sequence (series) and infinite geometric sequence (series). Chapter 2 handles the binomial coefficients and binomial theorem and show they how can be applied
to compute series sum. Chapter 3 deals with power series, including interchanging summation and differentiation; interchanging summation and integration; and generating function which expresses a sequence as coefficients arising from a power series in variables. Chapter 4 provides four methods of telescoping sum, including antidifference, partial fractions, trigonometric functions, and factorial functions. Chapter 5 discusses the telescoping product which the main ideas and techniques are analogous to telescoping sum. Two types of telescoping product including difference of two squares and trigonometric functions are investigated.
Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0623110-122025 |
Date | 23 June 2010 |
Creators | Lin, Yi-Ping |
Contributors | Mong-Na Lo Huang, May-Ru Chen, Fu-Chuen Chang, Mei-Hui Guo |
Publisher | NSYSU |
Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
Language | Cholon |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0623110-122025 |
Rights | not_available, Copyright information available at source archive |
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