Summation methods are techniques used to calculate the total of a sequence of numbers. These methods can be applied in various fields, including mathematics, statistics, and computer science. Common summation methods include the arithmetic series, geometric series, and numerical integration, each serving different purposes based on the nature of the data. In addition to basic summation, advanced techniques like the Euler-Maclaurin formula and Monte Carlo methods are used for more complex calculations. These methods help in approximating sums that may be difficult to compute directly, making them valuable tools in both theoretical and applied contexts.