What does the math notation $\sum$ mean?

Question

I have come across this symbol a few times, and I am not sure what it "does" or what it means: $\Large\sum$

Answer 1

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

$$\prod_{i=1}^5 i^2 $$