What does the math notation $\sum$ mean?
Here I use it once to explain what it does.
$$\sum_{i=1}^{5} i=1+2+3+4+5$$
Which translates to, sum over $i$, where $i$ starts at $1$ and goes to $5$. or this case
$$\sum_{i=1}^{5} i^2=1^2+2^2+3^2+4^2+5^2$$
Which translates to sum over the values of $i$, which range from $1$ to $5$ the function $i^2$.
Naturally one may wonder what if it is a product we are after, for example how do I represent $1\times2\times3\times4\times5$ or $1^2\times2^2\times3^2\times4^2\times5^2$
The notation for those are
$$\prod_{i=1}^5 i $$
and
$$\prod_{i=1}^5 i^2 $$
Coming from a programming background, I found it quite helpful to explain it using a for loop:
The mathematician would write it like this:
$\sum\limits_{i=m}^n f(i)$
And the programmer would write it like this:
result = 0
for (i=m; i<=n; i++) {
result += f(i)
}
You can think of m
as the start index
and n
as the end index
.