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 unique eludes us; yet we remain faithful to the ideal of it; and in spite of sense and of our merely abstract thinking, it becomes for us the most real thing in the actual world, although for us it is the elusive goal of an infinite quest.”
    —Josiah Royce (1855–1916)

    “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)