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:

    “Henry B. Adams was the first in an infinite series to discover and admit to himself that he really did not care whether truth was, or was not, true. He did not even care that it should be proved true, unless the process were new and amusing. He was a Darwinian for fun.”
    —Henry Brooks Adams (1838–1918)

    “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)