Convergence of a series

Definition

The convergence of a series is when the sum of its infinite terms approaches a finite limit. If this limit exists, the series is said to be convergent.

5 Must Know Facts For Your Next Test

1. The sum of a convergent series can be found using various tests like the Ratio Test and the Root Test.
2. A series must have its partial sums approach a finite number for it to converge.
3. If the terms of a series do not approach zero, the series cannot be convergent.
4. The Alternating Series Test can be used to determine the convergence of series with alternating positive and negative terms.
5. A geometric series converges if the absolute value of its common ratio is less than 1.

Review Questions

Related terms

Divergence:

A series that does not converge; its sum does not approach a finite limit.

Ratio Test:

A test used to determine the convergence or divergence of an infinite series by considering the limit of the absolute value of successive term ratios.

Partial Sum:

The sum of the first n terms in a sequence, which helps in analyzing whether an infinite series converges.