Convergence Behavior

Definition

Convergence behavior refers to the behavior of a mathematical sequence or series as its terms approach a certain value or as the number of terms increases. It determines whether the sequence or series approaches a specific limit, diverges to infinity, oscillates between values, or has no pattern at all.

Related terms

Divergence:

Divergence refers to the behavior of a sequence or series that does not approach any particular value but instead goes towards infinity or negative infinity.

Oscillation: Oscillation refers to the behavior of a sequence or series that alternates between two or more values without approaching any specific limit.

Convergent Sequence/Series: A convergent sequence/series is one that has a finite limit as its terms approach infinity (or as the number of terms increases).