Sigma notation (Summation)

$Σ$ This Greek symbol (called Sigma) means "sum up". It is the standard notation to write large sums.

You sum whatever is after the Sigma symbol:

$\sum 3 n$ in this case we would sum $3 n$ , called the summand. And $n$ is called the index of the sum.

But what values of $n$ do you sum?

The values are shown below and above the Sigma, and are referred as the limits of the sum.

$\sum_{n = 1}^{4} 3 n$
it says n goes from 1 (inferior limit) to 4 (superior limit), which is 1, 2, 3 and 4.

So now we add up the iteration of $n$ from 1 to 4, for the equation $3 n$ :
$\sum_{n = 1}^{4} 3 n = 3 (1) + 3 (2) + 3 (3) + 3 (4) = 30$

Properties of Sigma

We can factor a coefficient out of a sum:
$\sum_{k = m}^{n} c \cdot a_{k} = c \cdot \sum_{k = m}^{n} a_{k}$

For example, applying this property for the above summation, we have:
$\sum_{n = 1}^{4} 3 n = 3 \sum_{n = 1}^{4} n$

$\sum_{k = m}^{n} a_{k} \pm \sum_{k = m}^{n} b_{k} = \sum_{k = m}^{n} a_{k} \pm b_{k}$