Written by the Fiveable Content Team • Last updated September 2025
Verified for the 2026 exam
Verified for the 2026 exam•Written by the Fiveable Content Team • Last updated September 2025
Definition
Diverge refers to the behavior of a sequence or series where its terms do not approach any specific value or limit but instead grow infinitely larger or oscillate between different values.
Convergence is the opposite of divergence. It describes when a sequence or series approaches a specific value as more terms are added.
Oscillation: Oscillation refers to the repeated movement between two values without converging towards any particular one. It is often observed in sequences or series that diverge.
An infinite series is the sum of an infinite number of terms. Divergence plays a significant role in determining whether an infinite series has an infinite sum or does not converge at all.