converge

(noun)

Approach a finite sum.

Related Terms

Examples of converge in the following topics:

  • Infinite Geometric Series

    • A geometric series with a finite sum is said to converge.
    • A series converges if and only if the absolute value of the common ratio is less than one:
    • A formula can be derived to calculate the sum of the terms of a convergent series.
    • If a series converges, we want to find the sum of not only a finite number of terms, but all of them.

  • Summing the First n Terms in a Geometric Sequence

    • Historically, geometric series played an important role in the early development of calculus, and they continue to be central in the study of the convergence of series.
    • If $r$ is between $-1$ and $+1$, the terms of the series become smaller and smaller, approaching zero in the limit, and the series converges to a sum.

  • Applications of Geometric Series

    • Geometric series played an important role in the early development of calculus, and continue as a central part of the study of the convergence of series.
    • We now know that his paradox is not true, as evidenced by the convergence of the geometric series with $\displaystyle{r = \frac{1}{2}}$.

  • What Are Conic Sections?

    • In other words, it is a point about which rays reflected from the curve converge.

  • Introduction to Sequences

    • This sequence is neither increasing, nor decreasing, nor convergent.

  • The General Term of a Sequence

    • The computed differences have converged to a constant after the second sequence of differences.