How did the summation operation come into use? So we've been using summations at least since the dawn of calculus.  I'm wondering how the process of summing a function came to be known?  Are there events that led to the invention of the summation operation?  Can we attribute summations to a particular person, or persons?
How did mathematics evolve to include summation?
Less importantly, but still interesting, is how the summation symbol, $\sum$, came to be used.
 A: according to this source, the summation symbol $\Sigma$ was first used by Leonhard Euler in 1755:
Quemadmodum ad differentiam denotandam usi sumus signo $\Delta$, ita summam indicabimus signo $\Sigma$.
In the same way that we use the symbol $\Delta$ to denote a difference, we will indicate a sum by the symbol $\Sigma$.
[Institutiones calculi differentialis chapter I, paragraph 26.]

in a similar way one has [...], so that, if for $\sum x^2$, $\sum x$ and $\sum 1$ we substitute the values obtained previously, one finds that [...].
A: According to http://en.wikipedia.org/wiki/Binomial_theorem, a special case of the binomial theorem (i.e. for the exponent 2), was already known to Euclid as early as the 4th century B.C. and, as binomial coefficients surface when switching between the product- and the sum-formulation of polynomials, it seems reasonable to claim that summation as a representation of functions is tied to investigations on polynomials. 
Other milestones were Newton's 1665 generalization of the binomial theorem to non-integral exponents and later James Gregory's and Brook Taylor's discovery, that certain functions can be converted into a series via a combination of interpreting the function as an infinite polynomial with repeated differentiationg and evaluation at 0.  
A: We've been adding things up since the dawn of arithmetic.  The Pythagoreans knew all about figurate numbers, and how these were built up from gnomons: all they lacked was our current terminology and notation.  
