Sum
The sum of two numbers is generally speaking what we get when we add several numbers together. This operation is called additive summation or addition. There are a number of ways of writing sums, with the most common being:
- Addition ()
- Summation ()
- Computerization:
- Sum = 0
- For I = M to N
- Sum = Sum + X(I)
- Next I (in Visual BASIC)
There are types of summing, chiefly:
- additive summation ("adding")
- divisive summation ("dividing")
- factorial summation ("taking the factorial")
- fractional summation ("as a fraction")
- multiplicative summation or product summing
- percentile summation ("percent of" / "per cent. of" ; 2nd spelling termed archaic)
- root summation ("rooting")
- subtractive summation ("subtracting" or "minusing")
Sigma notationEdit
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 [1]) 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.[2]
PropertiesEdit
ApplicationsEdit
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:
Related pagesEdit
ReferencesEdit
- ↑ "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.
Further readingEdit
- Nicholas J. Higham, "The accuracy of floating point summation", SIAM J. Scientific Computing 14 (4), 783–799 (1993).
Other websitesEdit
- 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