Moving past sequences, we now look at summations. A summation, as the name implies, is the addition of a sequence of numbers.

As discussed earlier, sequences are ordered. Summations, which add up the terms of a sequence are also ordered; however, they use a special notation to create a shorthand description. Example:

$\sum\limits_{i=1}^{n}i$

Where i = 1 is the initial value, n is the terminal or “stop” value, and i by itself is the description of a single element of the sequence we will sum. Suppose the value given for n is not a number, but infinity, in that case we see an infinite series. Sometimes an infinite series will converge to a target value, such as the example of the natural root e we saw earlier. Note that we are not always this fortunate with summations, in many cases an infinite series summation will be infinity.