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:

    “Three elements go to make up an idea. The first is its intrinsic quality as a feeling. The second is the energy with which it affects other ideas, an energy which is infinite in the here-and-nowness of immediate sensation, finite and relative in the recency of the past. The third element is the tendency of an idea to bring along other ideas with it.”
    —Charles Sanders Peirce (1839–1914)

    “Life ... is not simply a series of exciting new ventures. The future is not always a whole new ball game. There tends to be unfinished business. One trails all sorts of things around with one, things that simply won’t be got rid of.”
    —Anita Brookner (b. 1928)