#Solving sequences an how to#
In this chapter you will learn how to prove summation formulae, such as the sum of n natural numbers and the sum of their squares or cubes using different methods including a geometric approach known to ancient Greeks and Babylonians. Figurate numbers (triangular, square, pentagonal, etc) will be introduced from a modern and ancient point of view, in both algebraic and geometric ways.
#Solving sequences an series#
You will learn interesting methods of finding the nth term and partial sums for series that are not geometric or arithmetic. The famous Fibonacci type sequences are demonstrated and different methods of finding formulae for the nth term of a recursive sequence are given as well as methods of finding recursive formulae for other known series.
Arithmetic and geometric progressions are studied in depth and many problems including some Olympiad type problems are given and solved. Increasing, decreasing, bounded, convergent, and divergent sequences are discussed at an elementary level suitable for an eighth grade student. The first chapter introduces sequences and series and their important properties. It can also be used by faculty who are looking for interesting and insightful problems that are not commonly found in other textbooks.
With nearly 300 problems including hints, answers, and solutions, Methods of Solving Sequences and Series Problems is an ideal resource for those learning calculus, preparing for mathematics competitions, or just looking for a worthwhile challenge. Intuitive and visual arguments are presented alongside technical proofs to provide a well-rounded methodology. The text aims to expand the mind of the reader by often presenting multiple ways to attack the same problem, as well as drawing connections with different fields of mathematics. Proof techniques are emphasized, with a variety of methods presented. Some problems are taken directly from mathematics competitions, with the name and year of the exam provided for reference.
The reader will find the problems interesting, unusual, and fun, yet solved with the rigor expected in a competition. The author, an accomplished female mathematician, achieves this by taking a problem solving approach, starting with fascinating problems and solving them step by step with clear explanations and illuminating diagrams. This book aims to dispel the mystery and fear experienced by students surrounding sequences, series, convergence, and their applications.
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