# Section 4.1 Sequences and Series

In formal terms, a complex sequence is a function whose domain is the positive integers and whose range is a subset of the complex numbers. For convenience, we at times use the term sequence rather than complex sequence.
If we wish a function s; to represent an arbitrary sequence, we could specify it by writing s(1) = z[1];, s(2) = z[2];, and so on. The values z[1], z[2], z[3];, ..., are called the terms of a sequence, and mathematicians, being generally lazy when it comes to things like this, often refer to z[1], z[2], z[3];, etc., as the sequence itself, even though they are really speaking of the range of the sequence when they do this. Mathematicians are also not so fussy about starting a sequence at z[1], so that z[0];, z[1];, z[2];, ..., etc., would also be acceptable notation, provided all terms were defined.