Summation/Sigma notation There are lots of variants in the notation for summation. For example, $$\sum_{k=1}^{n} f(k), \qquad \sum_{p \text{ prime}} \frac{1}{p}, \qquad \sum_{\sigma \in S_n} (\operatorname{sgn} \sigma) a_{1 , \sigma(1)} \ldots a_{n , \sigma(n)}, \qquad \sum_{d \mid n} \mu(d).$$ 
What exactly is a summation? How do we define it? Is there a notation that generalizes all of the above, so that each  of the above summations is a variant of the general notation? Are there any books that discuss this matter? 
It seems that summation is a pretty self-evident concept, and I have yet to find a discussion of it in a textbook. 

The wikipedia explains this (I think) pretty well, give it a try:
http://en.wikipedia.org/wiki/Summation#Notation
