Which Greek letter is used to mean 'sum of' in mathematics?

Capital sigma is the summation sign, chosen because sigma is the Greek S and sum starts with S. Leonhard Euler popularised the notation in the eighteenth century. Underneath the symbol you write the index and its starting value, above it the ending value, and to the right the expression being added, so the notation compresses a long addition into one compact line. Writing the sum of the first hundred squares is a single short expression rather than a hundred terms. The same idea appears in capital pi for products, using the Greek P, and both are used constantly in statistics, probability and calculus. Lower case sigma has a separate job in statistics, standing for the standard deviation of a population, which is why the phrase six sigma refers to a distance from the average. Greek letters are used throughout mathematics precisely because they add a second alphabet without colliding with ordinary variables.

Capital pi plays the same role for repeated multiplication that sigma plays for repeated addition.