CAPITAL SIGMA NOTATION Meaning and
Definition
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Capital sigma (Σ) notation is a mathematical notation used to represent the sum of a series or sequence of numbers. It is derived from the Greek letter sigma, which corresponds to the English letter S. Capital sigma notation allows for a concise and compact way of expressing summation, making it easier to represent large quantities of numbers.
In capital sigma notation, the symbol Σ is followed by the starting value of the index (usually denoted as an integer or a variable) underneath it, and an expression representing the value of each term in the summation is written to the right of the Σ symbol. The index value is increased by increments usually placed above and below the Σ symbol. The final value of the index is written above the Σ symbol. This notation allows for flexibility in terms of the range of the index.
The notation serves to compactly represent repetitive addition. As the index varies according to the specified range, the expression representing each term is evaluated, and the results of these evaluations are added together. This sum represents the overall value of the series. Capital sigma notation is commonly used in various branches of mathematics, including calculus, probability, and statistics, to represent the sum of numbers in equations, formulas, and calculations. It is particularly useful when the series contains a large number of terms or when a pattern for the terms can be identified.
