Convergent Series
In mathematics, a series is the sum of the terms of a sequence of numbers.
Given a sequence, the nth partial sum is the sum of the first n terms of the sequence, that is,
A series is convergent if the sequence of its partial sums converges. In more formal language, a series converges if there exists a limit such that for any arbitrarily small positive number, there is a large integer such that for all ,
A series that is not convergent is said to be divergent.
Read more about Convergent Series: Examples of Convergent and Divergent Series, Convergence Tests, Conditional and Absolute Convergence, Uniform Convergence, Cauchy Convergence Criterion
Famous quotes containing the word series:
“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)