This book teaches by solving problems. It is intended as a companion to standard textbooks for calculus students in learning sequences and infinite series. The first part of each section presents the definitions and theorems (without proofs) necessary for problem solving, and sometimes followed by comments or remarks. These definitions and theorems correspond to those given in most calculus textbooks, where all concepts and theorems are followed by explanations and proofs. The second part contains problems and complete solutions solved in such a simple way that the students find no difficulty to understand. The book contains over 450 solved problems. They can be used as practicing study guides by students and as supplementary teaching sources by instructors. Since the problems have very detailed solutions, they are helpful for under-prepared students.