This book, Sequences, and Series provides a modern introduction to sequences and series that focuses on conceptual understanding in developing a recursive and explicit formula for a given sequence and finding the sum of all of the terms of both finite and infinite series. All of the formulas in this book are provided with their proof as well for readers to have a deep understanding of each topic. We have used a conversational style of writing that gives a detailed explanation of the theorems, proofs, examples, and solutions. At the end of each chapter general review questions and their solutions are provided. We believe that this book will be a great resource for students who want to compete in math contests because one of the main topics of middle school and high school competitions is sequences and series. The theorems about developing a recursive formula for a given sequence are derived by the author by using Newton's little formula, Hockey's stick pattern and binomial expansion.

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