Continued Fractions and Series
Euler proved the following identity:
From this many other results can be derived, such as
and
Euler's formula connecting continued fractions and series is the motivation for the fundamental inequalities, and also the basis of elementary approaches to the convergence problem.
Read more about this topic: Generalized Continued Fraction
Famous quotes containing the words continued and/or series:
“Contrariwise, continued Tweedledee, if it was so, it might be; and if it were so, it would be; but as it isnt, it aint. Thats logic.”
—Lewis Carroll [Charles Lutwidge Dodgson] (18321898)
“Galileo, with an operaglass, discovered a more splendid series of celestial phenomena than anyone since.”
—Ralph Waldo Emerson (18031882)