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William L. Hosch
Former Encyclopædia Britannica Editor
BIOGRAPHY

William L. Hosch was an editor at Encyclopædia Britannica.

Primary Contributions (151)
Graphical illustration of an infinite geometric seriesClearly, the sum of the square's parts (12, 14, 18, etc.) is 1 (square). Thus, it can be seen that 1 is the limit of this series—that is, the value to which the partial sums converge.
Geometric series, in mathematics, an infinite series of the form a + ar + ar2 + ar3+⋯, where r is known as the common ratio. A simple example is the geometric series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +⋯, which converges to a sum of 2 (or 1 if the first term is excluded). The Achilles…
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