nth Root - Infinite Series

Infinite Series

The radical or root may be represented by the infinite series:

(1+x)^{s/t} = \sum_{n=0}^\infty \frac{\prod_{k=0}^{n-1} (s-kt)}{n!t^n}x^n

with . This expression can be derived from the binomial series.

Read more about this topic:  nth Root

Famous quotes containing the words infinite series, infinite and/or series:

    “In the order of literature, as in others, there is no act that is not the coronation of an infinite series of causes and the source of an infinite series of effects.”
    —Jorge Luis Borges (1899–1986)

    “The radio ... goes on early in the morning and is listened to at all hours of the day, until nine, ten and often eleven o’clock in the evening. This is certainly a sign that the grown-ups have infinite patience, but it also means that the power of absorption of their brains is pretty limited, with exceptions, of course—I don’t want to hurt anyone’s feelings. One or two news bulletins would be ample per day! But the old geese, well—I’ve said my piece!”
    —Anne Frank (1929–1945)

    “As Cuvier could correctly describe a whole animal by the contemplation of a single bone, so the observer who has thoroughly understood one link in a series of incidents should be able to accurately state all the other ones, both before and after.”
    —Sir Arthur Conan Doyle (1859–1930)