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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 notation[change | change source]

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]

Properties[change | change source]


Applications[change | change source]

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 pages[change | change source]

References[change | change source]

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

Further reading[change | change source]

Other websites[change | change source]