Is Sigma $\Sigma$ a mathematical way of doing a for loop? I've been a programmer for ten years, and once upon a time I was pretty good at math. Those days are long gone. I'm taking some online classes and now I find myself needing to remember the math I learned in college and it has all gone bye-bye.
Specifically, I have a question about $\Sigma$ (Sigma):
In an $\Sigma$ equation, there is an N above the $\Sigma$, and an $i = 1$ (or some number) below. 
If someone could help my programmer mind - this looks like a for loop in programming. Is that essentially what is going on with everything inside the $()$ of the $\Sigma$? It simply computes all the values for each iteration from $i$ to N and then sums them all up? 

In Mathematica I frequently switch between the Sum and the Table commands like in these examples:
Example 1:
$\sum\limits_{n=1}^{n=1} 1 = 1 = 1 $   
$\sum\limits_{n=1}^{n=2} 1 = 2 = 1+1 $   
$\sum\limits_{n=1}^{n=3} 1 = 3 = 1+1+1 $  
$\sum\limits_{n=1}^{n=4} 1 = 4 = 1+1+1+1 $  
$\sum\limits_{n=1}^{n=5} 1 = 5 = 1+1+1+1+1 $  
Sum[1,{n,1,5}]

which outputs: 5
compared to:
Table[1,{n,1,5}]

which outputs: {1,1,1,1,1}
Example 2:
$\sum\limits_{n=1}^{n=1} n = 1 = 1 $   
$\sum\limits_{n=1}^{n=2} n = 3 = 1+2$  
$\sum\limits_{n=1}^{n=3} n = 6 = 1+2+3$  
$\sum\limits_{n=1}^{n=4} n = 10 = 1+2+3+4$   
$\sum\limits_{n=1}^{n=5} n = 15 = 1+2+3+4+5$  
Sum[n,{n,1,5}]

which outputs: 15
compared to:
Table[n,{n,1,5}]

which outputs: {1,2,3,4,5}
Example 3:
$\sum\limits_{n=1}^{n=1} \frac{n(n+1)}{2} = 1 = 1$
$\sum\limits_{n=1}^{n=2} \frac{n(n+1)}{2} = 4 = 1+3$
$\sum\limits_{n=1}^{n=3} \frac{n(n+1)}{2} = 10 = 1+3+6$
$\sum\limits_{n=1}^{n=4} \frac{n(n+1)}{2} = 20 = 1+3+6+10$
$\sum\limits_{n=1}^{n=5} \frac{n(n+1)}{2} = 35 = 1+3+6+10+15$
Sum[n*(n+1)/2,{n,1,5}]

which outputs: 35
compared to:
Table[n*(n+1)/2,{n,1,5}]

which outputs: {1, 3, 6, 10, 15}
I don't know if it is a good answer to your question though.
