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)

    “Nothing could his enemies do but it rebounded to his infinite advantage,—that is, to the advantage of his cause.... No theatrical manager could have arranged things so wisely to give effect to his behavior and words. And who, think you, was the manager? Who placed the slave-woman and her child, whom he stooped to kiss for a symbol, between his prison and the gallows?”
    —Henry David Thoreau (1817–1862)

    “History is nothing but a procession of false Absolutes, a series of temples raised to pretexts, a degradation of the mind before the Improbable.”
    —E.M. Cioran (b. 1911)