összesítést

összesítést, or "summation" in English, refers to the mathematical process of adding a sequence of numbers together. It is a fundamental concept in algebra and calculus, often represented using the summation symbol (Σ). The term originates from Hungarian, where "össze" means "together" and "síteni" means "to add."

In mathematics, summation is used to calculate the total of a series of terms, which can be finite or infinite. For example, the sum of the first *n* natural numbers can be expressed as the summation of the sequence 1, 2, 3, ..., *n*. This process is particularly useful in various fields, including physics, engineering, statistics, and economics, where aggregating values is essential for analysis.

The summation symbol (Σ) is introduced by the German mathematician Gottfried Wilhelm Leibniz in the 17th century. It allows for concise notation of repeated addition, making complex calculations more manageable. A general summation is written as Σ *f*(*i*) from *i* = *a* to *b*, where *f*(*i*) represents the term being summed, and *a* and *b* define the range of summation.

In calculus, summation is closely related to integration, as the Riemann integral can be interpreted as the limit of a summation. This connection is foundational in understanding continuous functions through discrete approximations.

In everyday contexts, summation is applied in various computations, such as calculating totals in financial spreadsheets, determining averages, or processing data in statistical models. Its principles are also foundational in computer science, particularly in algorithms that require iterative addition, such as those used in sorting or searching.