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  2. AP Calculus
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Infinite Sequences and Series (BC Only)

Question 1
Calculus AB/BCAPConcept Practice
1 mark

Which of the following represents a sequence?

Question 2
Calculus AB/BCAPConcept Practice
1 mark

Determine the 10th term of the geometric sequence: 2, 6, 18, 54, ...

Question 3
Calculus AB/BCAPConcept Practice
1 mark

Identify the type of series and find the sum of the series: 1 + 1/3 + 1/9 + 1/27 + ...

Question 4
Calculus AB/BCAPConcept Practice
1 mark

Determine if the series ∑(n/(n+1))∑ (n/(n+1))∑(n/(n+1)) diverges using the nth term test.

Question 5
Calculus AB/BCAPConcept Practice
1 mark

Explain why the nth term test is inconclusive for the series ∑(1/n)∑ (1/n)∑(1/n).

Question 6
Calculus AB/BCAPConcept Practice
1 mark

Consider the series ∑(n22n)∑ (\frac{n^2}{2^n})∑(2nn2​). Can the nth term test determine the convergence or divergence of this series?

Question 7
Calculus AB/BCAPConcept Practice
1 mark

Use the Limit Comparison Test to determine the convergence or divergence of the series ∑(1/(n2+1))∑ (1/(n^2 + 1))∑(1/(n2+1)) by comparing it to the series ∑(1/n2)∑ (1/n^2)∑(1/n2).

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Question 8
Calculus AB/BCAPConcept Practice
1 mark

Determine the convergence or divergence of the series ∑(3n+1n3−2)∑ (\frac{3n+1}{n^3-2})∑(n3−23n+1​) using the Limit Comparison Test.

Question 9
Calculus AB/BCAPConcept Practice
1 mark

Determine the convergence or divergence of the series ∑n3+1n2∑ \frac{\sqrt{n^3 + 1}}{n^2}∑n2n3+1​​ using the Limit Comparison Test.

Question 10
Calculus AB/BCAPConcept Practice
1 mark

Apply the Direct Comparison Test to the series ∑(1/(n3+1))∑ (1/(n^3 + 1))∑(1/(n3+1)) by comparing it to a known convergent or divergent series.