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Date: Thu, 8 Oct 1998 15:08:58 -0400
From: Alex Bogomolny
This is a divergent series which has no sum. Some great people thought the sum was 1/2 (from S = 1 - S) but by the same token it could be declared 0 or 1. A history book is right to mention this phenomenon lest people think that mathematics is cast in stone. The notion of convergency/divergency was conceived as late as the second half of the 19th century. Since then it became clear that no value may be assigned to divergent series.
Best regards,
Alexander Bogomolny
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