URN 
etd0623110122025 
Author 
YiPing Lin 
Author's Email Address 
No Public. 
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Department 
Applied Mathematics 
Year 
2009 
Semester 
2 
Degree 
Master 
Type of Document 

Language 
zhTW.Big5 Chinese 
Title 
Sequences and Summation and Product of Series 
Date of Defense 
20100528 
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 
MeiHui Guo  chair
MongNa Lo Huang  cochair
MayRu Chen  cochair
FuChuen Chang  advisor

Files 
indicate not accessible 
Date of Submission 
20100623 