Understanding Mathematical Symbols – Summation (Addition)

When a summation over a range of numbers is to be presented it is not uncommon to shorthand the notation using the Sigma (the letter S in Greek, written as a Big E with the middle t replaced by a less than symbol $\Sigma$). For example, the following sums can be represented in the Sigma notation as follows:

Example 1:

$$1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 61$$ Can be written as: $$\sum_{n\ =\ 1}^{10}n=61$$

Example 2:

$$2 + 4 + 6 + 8 + 10 = 30[latex]

Can be written as:

[latex display="true"]\sum_{n\ =\ 1}^{5}2n=30$$
or $$\sum_{n\ =\ 1}^{5}2\times n=30$$

Interesting, in defining an example for the Sigma (summation) notation more fancy notation was introduced.

The first notation that is encountered in Example 1, is the small numbers at the top and bottom of the Sigma symbol. Starting the from the bottom equation, $n=1$, the notation states that a variable $n$ is going to be used with a value assigned to $1$. Next the top value, $10$, indicates that the variable, $n$, will be increased until the value $10$. Thus, the notation in Example 1 can be read as "The sum of n starting from 1 to 10 is 61".

In the second example, there is another mathematical shorthand. When a number is multiplied by a variable, like in the example above 2 is multiplied (times) the variable $n$. In Mathematics it is common to remove the multiplier symbol ($\times$) and write the number and the variable together. Thus, $2\times n$ can be written as $2n$. Note that this notation is also used when multiplying two variables. However, in this case one has to be careful that the notation won’t confuse the readers.