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)

    “That man’s best works should be such bungling imitations of Nature’s infinite perfection, matters not much; but that he should make himself an imitation, this is the fact which Nature moans over, and deprecates beseechingly. Be spontaneous, be truthful, be free, and thus be individuals! is the song she sings through warbling birds, and whispering pines, and roaring waves, and screeching winds.”
    —Lydia M. Child (1802–1880)

    “Mortality: not acquittal but a series of postponements is what we hope for.”
    —Mason Cooley (b. 1927)