addition of a sequence of numbers

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 ()
  • Code:
Sum = 0
For I = M to N
Sum = Sum + X(I)
Next I (in Visual BASIC)

Sigma notation


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]





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:



  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

  • Nicholas J. Higham, "The accuracy of floating point summation", SIAM J. Scientific Computing 14 (4), 783–799 (1993).

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