© 2016

Methods of Solving Sequence and Series Problems


  • Ideal for independent study, competition training, or as an extra resource in the classroom

  • Contains nearly 300 problems with answers, hints, and detailed solutions

  • Includes fascinating special topics related to sequences and series not usually covered in calculus classes


Table of contents

  1. Front Matter
    Pages i-xx
  2. Ellina Grigorieva
    Pages 1-63
  3. Ellina Grigorieva
    Pages 65-121
  4. Ellina Grigorieva
    Pages 123-190
  5. Ellina Grigorieva
    Pages 227-269
  6. Back Matter
    Pages 271-281

About this book


This book aims to dispel the mystery and fear experienced by students surrounding sequences, series, convergence, and their applications. 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.

The reader will find the problems interesting, unusual, and fun, yet solved with the rigor expected in a competition. Some problems are taken directly from mathematics competitions, with the name and year of the exam provided for reference.  Proof techniques are emphasized, with a variety of methods presented.  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. Intuitive and visual arguments are presented alongside technical proofs to provide a well-rounded methodology.

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. It can also be used by faculty who are looking for interesting and insightful problems that are not commonly found in other textbooks.   


Sequences and Series Calculus Calculus Practice Problems Applications of Sequences Series Convergence Convergence Tests Math Competitions

Authors and affiliations

  1. 1.Department of Mathematics and Computer ScienceTexas Woman’s UniversityDentonUSA

About the authors

Ellina Grigorieva, PhD, is Professor of Mathematics at Texas Women's University, Denton, TX, USA

Bibliographic information


“The charm of this book is that it showcases a lot of problems that can be solved by ingenuity and elementary methods. … It does a good job of addressing the common problem that students can quote the test but can only apply it if the series has exactly the form of that test. … The writing is clear and there is a good narrative flow to keep you moving through what is essentially a series of worked problems.” (Allen Stenger, MAA Reviews,, March, 2017)

“The volume is mainly intended for students studying the basic principles of analysis. It should be especially helpful to teachers using the book as a text and to students using the book as a reference. The volume can also be used by faculty who are looking for interesting and insightful problems that are not commonly found in other textbooks. The volume is also suitable for self-study.” (Teodora-Liliana Rădulescu, zbMath 1367.40001, 2017)