ADVANCED APPROACHES TO SUMMATION IN MATHEMATICAL EDUCATION
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This article explores the theoretical and practical aspects of efficiently and optimally calculating certain types of mathematical sums that are widely used in mathematical analysis and algebraic structures. Since secondary school mathematics textbooks typically address only basic summation cases using arithmetic or geometric progression formulas, students are often limited to solving simple summation problems. As a result, they face difficulties when encountering more complex expressions. In this study, general formulas for various types of sums, their mathematical proofs, conditions of applicability, and illustrative examples are thoroughly discussed. In addition, several problems related to identities and summations frequently encountered in contemporary mathematical olympiads and academic competitions are analyzed. This work serves as a theoretical and methodological resource for teaching mathematics, developing computational algorithms, and enhancing students’ mathematical thinking.[1-5].
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