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.

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Famous quotes containing the words 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.
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    As Cuvier could correctly describe a whole animal by the contemplation of a single bone, so the observer who has thoroughly understood one link in a series of incidents should be able to accurately state all the other ones, both before and after.
    Sir Arthur Conan Doyle (1859–1930)