ABSTRACT
We select 12 infinite series problems that have appeared in the Monthly and try to present solutions in a cohesive and engaging way. Through various solutions and proofs, we illustrate how problem-solving evolve over time — from the specific to the general, from the simplified scenario to the theoretical framework, from the concrete to the abstract. You may find some problems ultimately reach results related to current research. Along the way, we hope you can learn how to solve hard problems and the motivation behind them, and expand the breadth and depth of your mathematical knowledge.
