Sequences and Series
In this chapter, we consider three important types of sequences: arithmetic sequences, geometric sequences, and the harmonic sequence. In an arithmetic sequence, the difference between consecutive elements is constant. In a geometric sequence, the ratio between consecutive elements is constant. The harmonic sequence is simply the sequence (1, , , … ).
Given a sequence (x0, x1, … ), we may wish to define a new sequence that consists of the partial sums
The sequence (y0, y1, … ) of partial sums is a series.