A Short Book on Long Sums: Infinite Series for Calculus Students

This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes understanding the fundamental ideas. Power series—and infinite series in general—are a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural.

Calculus is about functions, so the book turns on two fundamental ideas: using polynomials to a...