As A Continued Fraction
Euler proved that the number e is represented as the infinite simple continued fraction (sequence A003417 in OEIS):
Its convergence can be tripled by allowing just one fractional number:
Here are some infinite generalized continued fraction expansions of e. The second is generated from the first by a simple equivalence transformation.
This last, equivalent to, is a special case of a general formula for the exponential function:
Read more about this topic: List Of Representations Of E
Famous quotes containing the words continued and/or fraction:
“The problems of society will also be the problems of the predominant language of that society. It is the carrier of its perceptions, its attitudes, and its goals, for through it, the speakers absorb entrenched attitudes. The guilt of English then must be recognized and appreciated before its continued use can be advocated.”
—Njabulo Ndebele (b. 1948)
“The mother as a social servant instead of a home servant will not lack in true mother duty.... From her work, loved and honored though it is, she will return to her home life, the child life, with an eager, ceaseless pleasure, cleansed of all the fret and fraction and weariness that so mar it now.”
—Charlotte Perkins Gilman (1860–1935)