converge

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.