How Euler Did It

Модератор: mike@in-russia

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J.F.

How Euler Did It

Номер сообщения:#1   J.F. » Сб авг 09, 2008 20:44

How Euler Did It

http://www.maa.org/editorial/euler/How% ... series.pdf

E-72 is Euler?s first paper that closely follows the modern Theorem-Proof format. There are no definitions in the paper, or it would probably follow the Definition-Theorem-Proof format. After an
introductory paragraph in which Euler tells part of the story of the problem, Euler gives us a theorem
and a proof:
?Theorem 1. This infinite series, continued to infinity,
1/3+ 1/7+ 1/8+1/15+ 1/24+ 1/26+ 1/31+ 1/35 1+etc.
the denominators of which are all numbers which are one less than powers of degree two or higher of
whole numbers, that is, terms which can be expressed with the formula
1/m^n -1, where m and n are
integers greater than one, then the sum of this series is = 1.?

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