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)

    “[The human mind] finds more facility in assenting to the self-existence of an invisible cause possessing infinite power, wisdom, and goodness, than in the self-existence of the universe, visibly destitute of these attributes, and which may be the effect of them.”
    —James Madison (1751–1836)

    “I look on trade and every mechanical craft as education also. But let me discriminate what is precious herein. There is in each of these works an act of invention, an intellectual step, or short series of steps taken; that act or step is the spiritual act; all the rest is mere repetition of the same a thousand times.”
    —Ralph Waldo Emerson (1803–1882)