Sequences, Combinations, Limits

A Classic Approach to High School Mathematics 📐

Originally published as Volume 3 of the Library of School Mathematics, this collection of problems offers a distinctive path into sequences, combinatorial reasoning, and limits. Instead of a traditional textbook, the authors present carefully chosen problems that encourage active exploration and proof.

The material was developed for ninth and tenth grade students in Moscow mathematics schools, but its clarity and emphasis on understanding make it useful for any learner who wants to build stronger mathematical thinking.

Three Core Topics, One Unified Method 🧮

The book is organized into three chapters, each with a clear problem-first structure:

• Sequences – including the method of mathematical induction and a wide range of practice problems.
• Combinations – combinatorial reasoning that requires no advanced algebra, making it approachable and engaging.
• Limits – from intuitive introductory problems to formal definitions and computational techniques.

Designed for Independent Study

Every problem is accompanied by answers, hints, or full solutions. The authors encourage readers to attempt problems before consulting the solutions, and they use helpful visual markers to flag important definitions, difficult passages, and common pitfalls. This structure supports both classroom use and self-directed learning.

Who Will Find This Book Valuable?

Students preparing for advanced mathematics, teachers seeking a rich bank of problems, and anyone who enjoys mathematical puzzles will appreciate the book’s rigorous yet inviting style. The emphasis on proof and understanding over rote computation makes it especially well suited for building a strong foundation in analysis and combinatorics.

From the Library of School Mathematics

This title is part of a series edited by I. M. Gelfand, known for its thoughtful, problem-centered approach to school mathematics. Each volume focuses on deepening conceptual understanding through carefully sequenced exercises.