Sum

addition of a sequence of numbers

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

 
 
 
 [3]
 [3]
 [3]
 

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

  1. "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-08-16.
  2. Weisstein, Eric W. "Sum". mathworld.wolfram.com. Retrieved 2020-08-16.
  3. 3.0 3.1 3.2 "Calculus I - Summation Notation". tutorial.math.lamar.edu. Retrieved 2020-08-16.

Further readingEdit

Other websitesEdit