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

SERIES 199
we read it in the artistic way, gradually preparing the mind for the crisis of 500,000.
The ordinary process of numerical multiplication proceeds by means of the summation of a series. Consider the computation
342
658
2736
1710
2052
225036
Hence the three lines to be added form a
series of which the first term is the upper
line. This series follows the artistic method
of presenting the most important term last,
not from any feeling for art, but because of
the convenience gained by keeping a firm
hold on the units' place, thus enabling us to
omit some O's, formally necessary.
But when we approximate by gradually
adding the successive terms of an infinite
series, what are we approximating to? The
difficulty is that the series has no "sum" in
the straightforward sense of the word, because
the operation of adding together its terms
can never be completed. The answer is that
we are approximating to the limit of the
summation of the series, and we must now