### Capital-sigma notation

Mathematical notation has a special representation for compactly representing summation of many similar terms: the summation symbol ∑ (U+2211), a large upright capital Sigma. This is defined thus:

$\sum_{i=m}^n x_i = x_m + x_{m+1} + x_{m+2} +\dots+ x_{n-1} + x_n.$

The subscript gives the symbol for an index variable, i. Here, i represents the index of summation; m is the lower bound of summation, and n is the upper bound of summation. Here i = m under the summation symbol means that the index i starts out equal to m. Successive values of i are found by adding 1 to the previous value of i, stopping when i = n. An example:

$\sum_{k=2}^6 k^2 = 2^2+3^2+4^2+5^2+6^2 = 90$.

Informal writing sometimes omits the definition of the index and bounds of summation when these are clear from context, as in

$\sum x_i^2 = \sum_{i=1}^n x_i^2$.

One often sees generalizations of this notation in which an arbitrary logical condition is supplied, and the sum is intended to be taken over all values satisfying the condition. For example:

$\sum_{0\le k< 100} f(k)$

is the sum of f(k) over all (integer) k in the specified range,

$\sum_{x\in S} f(x)$

I often forget how to interpret the capital sigma symbol (∑) when I see it. This guide on Wikipedia is pretty useful.