AP Calculus BC · Unit 10: Infinite Sequences and Series
10.3 The nth Term Test for Divergence
In short
This topic introduces the nth term test, which is specifically and exclusively used as a test for divergence of a series. It is part of the BC ONLY curriculum. You are expected to apply this test to determine if a series diverges, understanding that it cannot be used to prove convergence.
Last updated
What else do you need to know about The nth Term Test for Divergence?
The focus is on applying the appropriate mathematical definition or test and justifying the conclusion.
Can you do these?
- I can use the nth term test to determine if a series diverges.
How is The nth Term Test for Divergence tested on the exam?
On the AP Exam, applying a convergence or divergence test requires explicit verification that all necessary conditions are met. A sound justification relies upon both mathematical evidence and reasons why that evidence supports the conclusion. You must consistently use correct notation and language to present solutions, explain reasoning, and justify conclusions.
Free practice questions with full explanations, and instant marking of your free-response answers.
The nth Term Test for Divergence: common questions
What do you need to know about The nth Term Test for Divergence for AP Calculus BC?
This topic introduces the nth term test, which is specifically and exclusively used as a test for divergence of a series. It is part of the BC ONLY curriculum. You are expected to apply this test to determine if a series diverges, understanding that it cannot be used to prove convergence.
How is The nth Term Test for Divergence tested on the AP Calculus BC exam?
On the AP Exam, applying a convergence or divergence test requires explicit verification that all necessary conditions are met. A sound justification relies upon both mathematical evidence and reasons why that evidence supports the conclusion.
How do I know I have mastered The nth Term Test for Divergence?
Check you can do each of these: use the nth term test to determine if a series diverges.
Where does The nth Term Test for Divergence fit in AP Calculus BC?
The nth Term Test for Divergence is topic 10.3 in Unit 10: Infinite Sequences and Series of AP Calculus BC.
Want help mastering this topic?
Work through The nth Term Test for Divergence one-on-one with an AP Guru tutor.
Book a free demo class