Geometric series (cross-reference)

The partial sums $S_n = a_0 + a_1 + \cdots + a_n$ form in turn a sequence, whose limit is called the sum of the series.

The geometric series $\displaystyle\sum_{n=0}^\infty q^n$ with $|q|<1$ converges to $\dfrac{1}{1-q}$: it is the fundamental case already met in Year Two (“geometric series of areas”), reformulated here as the limit of a sequence of sums.

This cross-reference closes the loop of the chapter: the limit of a sequence, introduced to understand “which number the terms tend to”, becomes the tool that gives meaning to the sum of infinitely many terms.

Links

Topics: Sequences
Concepts: Limit of a sequence · Geometric progression · Geometric series