An introduction to mathematics, by A. N. Whitehead.

CHAPTER XIV
SERIES
No part of Mathematics suffers more from
the triviality of its initial presentation to
beginners than the great subject of series.
Two minor examples of series, namely arithmetic and geometric series, are considered;
these examples are important because they
are the simplest examples of an important
general theory. But the general ideas are
never disclosed; and thus the examples,
which exemplify nothing, are reduced to
silly trivialities.
The general mathematical idea of a series
is that of a set of things ranged in order, that
is, in sequence. This meaning is accurately
represented in the common use of the term.
Consider, for example, the series of English
Prime Ministers during the nineteenth century, arranged in the order of their first tenure
of that office within the century. The series
commences with William Pitt, and ends with
Lord Rosebery, who, appropriately enough,
is the biographer of the first member. We
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