AP Calculus BC Flashcards: Determining Absolute or Conditional Convergence
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
If a series converges, but rearranging its terms changes its sum, what can you conclude?
The series is not absolutely convergent; it must be conditionally convergent.
Card 1 of 10
All Flashcards (10)
If a series converges, but rearranging its terms changes its sum, what can you conclude?
The series is not absolutely convergent; it must be conditionally convergent.
Define 'conditionally convergent' in relation to absolute convergence.
A series is conditionally convergent if it converges, but it does not converge absolutely.
A series is known to be absolutely convergent. What happens to its value if you regroup the terms?
The value of the series remains the same, as any regrouping of an absolutely convergent series has the same value.
Does convergence of a series imply absolute convergence?
No. A series can converge without being absolutely convergent, in which case it is called conditionally convergent.
What are the three possible classifications for the convergence of a series?
A series may be absolutely convergent, conditionally convergent, or divergent.
You test a series and find that it converges absolutely. What, if anything, do you now know about its convergence?
You know that the series converges, because any series that converges absolutely also converges.
What is a key property of an absolutely convergent series regarding the arrangement of its terms?
If a series converges absolutely, any series obtained by regrouping or rearranging its terms converges to the same value.
What is the relationship between absolute convergence and convergence?
If a series converges absolutely, then it is guaranteed to converge.
What is the foundational determination that must be made before classifying a series as absolutely or conditionally convergent?
One must first determine whether the series converges or diverges at all.
Which is a stronger condition for a series: convergence or absolute convergence?
Absolute convergence is a stronger condition, because if a series converges absolutely, then it must converge.