A summation is the addition of terms in a sequence, for summation to be possible every term that is being summed must be defined for the addition operation.

Notation

Where is the upper bound or the maximum value the summation is taken, if the summation is called a series. is the index, is the lower bound or the initial value for the index, and is the term in the sequence being summed.

Evaluation of Finite Sums

When a summation is taken over a finite range , it can be easily evaluated by taking every integer in the interval and evaluating the sequence for that number.

Formal Definition

The summation operation can be defined recursively as follows:

Example