Euler on infinite series

Divergent series

Leonhard Euler succinctly described a potential foundation for his treatment of divergent series in a calculus textbook published in 1755 [Euler (1755), Part 1, Chapter 3, #111, pp.78-79; English translation by Bromwich (p.322). Kline's translation (1983, p.313) is almost identical.] :

ee also

* the history of Grandi's series
* 1 − 1 + 1 − 1 + · · ·
* 1 − 2 + 4 − 8 + · · ·

Notes

References

*cite book |last=Bromwich |first=T.J. |year=1926 |origyear=1908 |edition=2e |title=An Introduction to the Theory of Infinite Series
*cite book |last=Euler |first=Leonhard |authorlink=Leonhard Euler |title=Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum |year=1755 |url=http://www.math.dartmouth.edu/~euler/pages/E212.html
*cite journal |last=Kline |first=Morris |authorlink=Morris Kline |title=Euler and Infinite Series |journal=Mathematics Magazine |volume=56 |issue=5 |year=1983 |month=November |pages=307–314 |url=http://links.jstor.org/sici?sici=0025-570X%28198311%2956%3A5%3C307%3AEAIS%3E2.0.CO%3B2-M


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