The sum of two numbers is their value added together. This operation is called additive summation or addition. There are many ways of writing sums, including:
- Addition ()
- Summation ()
- Sum = 0
- For I = M to N
- Sum = Sum + X(I)
- Next I (in Visual BASIC)
Sigma notation is a mathematical notation to write long sums in a short way. Sigma notation uses the Greek letter Sigma ( ), and takes upper and lower bounds which tell us where the sum begins and where it ends. The lower bound usually has a variable (called the index, often denoted by , or ) along with a value, such as " ". This tells us that the summation begins at 2, and goes up by 1 until it reaches the number on the top.
Sums are used to represent series and sequences. For example:
The geometric series of a repeating decimal can be represented in summation. For example:
The concept of an integral is a limit of sums, with the area under a curve being defined as:
- ↑ "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-08-16.
- ↑ Weisstein, Eric W. "Sum". mathworld.wolfram.com. Retrieved 2020-08-16.
- ↑ 3.0 3.1 3.2 "Calculus I - Summation Notation". tutorial.math.lamar.edu. Retrieved 2020-08-16.
- Nicholas J. Higham, "The accuracy of floating point summation", SIAM J. Scientific Computing 14 (4), 783–799 (1993).
- Media related to Summation at Wikimedia Commons
- Sigma Notation Archived 2015-09-21 at the Wayback Machine on PlanetMath
- Derivation of Polynomials to Express the Sum of Natural Numbers with Exponents Archived 2013-02-18 at the Wayback Machine