Title page for etd-0623110-122025


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URN etd-0623110-122025
Author Yi-Ping Lin
Author's Email Address No Public.
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Department Applied Mathematics
Year 2009
Semester 2
Degree Master
Type of Document
Language zh-TW.Big5 Chinese
Title Sequences and Summation and Product of Series
Date of Defense 2010-05-28
Page Count 110
Keyword
  • trigonometric functions
  • telescoping sum
  • telescoping product
  • Taylor's theorem
  • power series
  • partial fraction
  • series
  • sequence
  • Newton theorem
  • geometric sequence (series)
  • arithmetic sequence (series)
  • generating function
  • falling factorial
  • binomial theorem
  • antidifference
  • Abstract 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.
    Advisory Committee
  • Mei-Hui Guo - chair
  • Mong-Na Lo Huang - co-chair
  • May-Ru Chen - co-chair
  • Fu-Chuen Chang - advisor
  • Files
  • etd-0623110-122025.pdf
  • indicate not accessible
    Date of Submission 2010-06-23

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