SIGMA NOTATION Meaning and
Definition
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Sigma notation, also known as summation notation or the summation symbol, is a mathematical notation used to represent the sum of a series of numbers or terms. It is denoted by the Greek letter sigma (Σ), which stands for "sum."
In this notation, a series of terms is written inside the sigma symbol, along with an index or variable representing the lower value of the sum. The upper value of the sum is usually indicated above the sigma symbol. The index or variable takes on a range of values, which are used to determine the terms to be added together.
Sigma notation allows the concise representation of long sums or series, saving space and simplifying complex mathematical expressions. It is commonly used in various branches of mathematics, such as calculus, statistics, and discrete mathematics.
To evaluate a sum expressed in sigma notation, one needs to substitute each value of the index or variable into the expression representing the terms, and then add the results. The sum of the terms can also be expressed using a closed-form formula or a mathematical rule, depending on the nature of the series.
In summary, sigma notation is a compact and practical mathematical notation that represents the sum of a series of terms. It simplifies mathematical expressions and enables the concise representation, evaluation, and analysis of various types of summations.
Etymology of SIGMA NOTATION
The word "sigma" in "sigma notation" originates from the Greek alphabet, more specifically from the uppercase letter Σ (sigma). In mathematics, sigma notation denotes a way to compactly represent the sum of a series. The use of sigma notation started in the early 17th century, when the German mathematician Johann Faulhaber introduced the now widely-known summation symbol (∑) to represent the operation of summing a series of numbers. The symbol resembles the uppercase sigma in the Greek alphabet, and hence the name "sigma notation" evolved.
