Summation

Summation refers to the process of adding a sequence of numbers together to find their total. It's a fundamental operation in mathematics, statistics, and computer science, representing the accumulation of values over a defined range or set. The Summation process can be represented using the Summation symbol (∑), with indices indicating the starting and ending points of the sequence. The result of the Summation is a single value that represents the aggregate of all the individual terms in the sequence. Summation is utilized across many scientific and engineering fields for simplifying complex equations and calculating aggregate statistics.

Summation meaning with examples

• The Summation of the first ten natural numbers, from 1 to 10, yields a total of 55, which can be easily calculated using the formula n(n+1)/2 or simply by adding each number.
• In statistics, Summation is essential for calculating the mean of a dataset; you add all the values together and then divide by the number of values, giving you the average.
• When calculating the area under a curve using Riemann sums, we approximate the area by dividing it into many small rectangles and finding the Summation of the areas of each rectangle.
• In computer programming, a loop can be used to perform Summation of elements within an array or list, accumulating a running total of the element's value over each iteration.