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 and/or series:

    Vanity is as advantageous to a government as pride is dangerous. To be convinced of this we need only represent, on the one hand, the numberless benefits which result from vanity, as industry, the arts, fashions, politeness, and taste; and on the other, the infinite evils which spring from the pride of certain nations, a laziness, poverty, a total neglect of everything.
    —Charles Louis de Secondat Montesquieu (1689–1755)

    If the technology cannot shoulder the entire burden of strategic change, it nevertheless can set into motion a series of dynamics that present an important challenge to imperative control and the industrial division of labor. The more blurred the distinction between what workers know and what managers know, the more fragile and pointless any traditional relationships of domination and subordination between them will become.
    Shoshana Zuboff (b. 1951)