Browse Definitions :
Definition

# summation (sum)

A summation, also called a sum, is the result of arithmetically adding numbers or quantities. A summation always contains a whole number of terms. There can be as few as two terms, or as many as a hundred, a thousand, or a million. Some summations contain infinitely many terms.

For short sums, the numbers, or addends, can be written one after another, separated by addition signs (+). An example is 1/1 + 1/2 + 1/3. This becomes awkward when the number of terms is large. When a summation has infinitely many terms, the terms must occur in a definable sequence. This sequence is not always clear when the terms are simply listed and separated by + symbols. For this reason, the summation symbol was devised: a large, uppercase Greek letter sigma.

To denote 1/1 + 1/2 + 1/3, the following symbology can be used:

The expression on the left-hand side of the equation is the summation from n = 1 to n = 3 for 1/ n . The value of n is always an integer. It usually starts at 1 and always increases by 1 for each succeeding term in the summation.

Suppose the above series is extended without limit according to the obvious pattern. Then the summation from n = 1 to unlimited values of n for 1/ n , that is, 1/1 + 1/2 + 1/3 + 1/4 + ..., is denoted like this:

The sideways 8 means that n continues to increase without limit. It is imprecise to say we are dealing with the summation from n to infinity, but this terminology is often used anyway.

See our list of Mathematical Symbols .

This was last updated in March 2011
• Network as a Service (NaaS)

Network as a service, or NaaS, is a business model for delivering enterprise WAN services virtually on a subscription basis.

• network configuration management (NCM)

Network configuration management is the process of organizing and maintaining information about all of the components in a ...

• presentation layer

The presentation layer resides at Layer 6 of the Open Systems Interconnection (OSI) communications model and ensures that ...

• crypto wallet (cryptocurrency wallet)

A crypto wallet (cryptocurrency wallet) is software or hardware that enables users to store and use cryptocurrency.

• zero-day (computer)

A zero-day is a security flaw in software, hardware or firmware that is unknown to the party or parties responsible for patching ...

• backdoor (computing)

A backdoor attack is a means to access a computer system or encrypted data that bypasses the system's customary security ...

• team collaboration

Team collaboration is a communication and project management approach that emphasizes teamwork, innovative thinking and equal ...

• employee self-service (ESS)

Employee self-service (ESS) is a widely used human resources technology that enables employees to perform many job-related ...

• learning experience platform (LXP)

A learning experience platform (LXP) is an AI-driven peer learning experience platform delivered using software as a service (...