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:

    “The radio ... goes on early in the morning and is listened to at all hours of the day, until nine, ten and often eleven o’clock in the evening. This is certainly a sign that the grown-ups have infinite patience, but it also means that the power of absorption of their brains is pretty limited, with exceptions, of course—I don’t want to hurt anyone’s feelings. One or two news bulletins would be ample per day! But the old geese, well—I’ve said my piece!”
    —Anne Frank (1929–1945)

    “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)