# Summation Notation

## Key Questions

${\sum}_{n = 1}^{\infty} {a}_{n} = {a}_{1} + {a}_{2} + {a}_{3} + \ldots$

${\sum}_{n = 0}^{10} {n}^{2}$

#### Explanation:

The summation notation is mostly used to represents series or to express a series in a short form.

For example : if I want to write the series : $1 + 4 + 9 + 16 + 25$
in summation notation I would simply write:

${\sum}_{n = 1}^{5} {n}^{2}$

It depends on the brand of calculator you have.

#### Explanation:

The only calculator series I'm familiar with is the Casio fx series, so I'll give an answer based on them.

As far as I'm aware, Casio fx- 991ES and any calculator beyond that can perform summations using sigma notation.

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.