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)

    “And universal Nature, through her vast
    And crowded whole, an infinite paroquet,
    Repeats one note.”
    —Ralph Waldo Emerson (1803–1882)

    “Depression moods lead, almost invariably, to accidents. But, when they occur, our mood changes again, since the accident shows we can draw the world in our wake, and that we still retain some degree of power even when our spirits are low. A series of accidents creates a positively light-hearted state, out of consideration for this strange power.”
    —Jean Baudrillard (b. 1929)