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)

    “If I could only live at the pitch that is near madness
    When everything is as it was in my childhood
    Violent, vivid, and of infinite possibility:
    That the sun and the moon broke over my head.”
    —Richard Eberhart (b. 1904)

    “Galileo, with an operaglass, discovered a more splendid series of celestial phenomena than anyone since.”
    —Ralph Waldo Emerson (1803–1882)