# What is summation notation?

Jun 25, 2015

Summation is a shorthand way for writing long additions.

#### Explanation:

Say you want to add all numbers up to and including 50.
Then you could write out:
$1 + 2 + 3 + \ldots \ldots + 49 + 50$
(If you really write this out in full, it'll be a long line of numbers).

With this notation you would write:
${\sum}_{k = 1}^{50} k$
Meaning: sum up all the numbers $k$ from $1 \to 50$
The $\Sigma$-(sigma)-sign is the Greek letter for $S$ (sum).

Another example:
If you want to add all the squares from $1 \to 10$ you simply write:
${\sum}_{k = 1}^{10} {k}^{2}$
You see that this $\Sigma$-thing is a very versatile tool.