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 n is not given as a number. In that case, we see an infinite series, which converges to the target value. This technique provides us with a numerical method for approximating the target value (for example, the natural root e we saw earlier). Note that we are not always this fortunate with summations.