## 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:

The subscript gives the symbol for an index variable,

i. Here,irepresents theindex of summation;mis thelower bound of summation, andnis theupper bound of summation. Herei=munder the summation symbol means that the indexistarts out equal tom. Successive values ofiare found by adding 1 to the previous value ofi, stopping wheni=n. An example:

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

- .
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:

is the sum of

f(k) over all (integer)kin the specified range,

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