AP Calculus BC Unit 10 practice questions: Infinite Sequences and Series
11 original multiple-choice questions on AP Calc BC Unit 10, infinite sequences and series. Answer each one in your browser and read the explanation, then review the key ideas below.
Question 1 of 11
What is the sum of the geometric series Σ from n = 0 to ∞ of (1/3)ⁿ?
Question 2 of 11
Which series converges?
Question 3 of 11
What is the radius of convergence of Σ xⁿ/3ⁿ?
Question 4 of 11
What is the Maclaurin series for eˣ?
Question 5 of 11
What is the second-degree Taylor polynomial for cos x centered at x = 0?
Question 6 of 11
The alternating series Σ (−1)ⁿ⁺¹/n is estimated by its first 4 terms. What bound does the alternating series error bound give?
Question 7 of 11
For a series Σ aₙ, lim (n→∞) |aₙ₊₁/aₙ| = 1/2. What does the ratio test tell you?
Question 8 of 11
What is the interval of convergence of Σ from n = 1 to ∞ of xⁿ/n?
Question 9 of 11
What is the third-degree Maclaurin polynomial for sin x?
Question 10 of 11
How does Σ from n = 1 to ∞ of (−1)ⁿ⁺¹/n behave?
Question 11 of 11
For a series Σ aₙ, lim (n→∞) aₙ = 0. What can you conclude?
Key ideas in Unit 10
- A series converges if its partial sums approach a limit. If the terms don't go to 0, the series diverges (nth-term test), but terms going to 0 is not enough.
- Geometric series Σ arⁿ converge to a/(1 − r) when |r| < 1; p-series Σ 1/nᵖ converge when p > 1.
- Know the integral, comparison, limit comparison, alternating series and ratio tests, and when each applies.
- Absolute versus conditional convergence: the alternating harmonic series converges, but its absolute values don't.
- Taylor and Maclaurin series approximate functions with polynomials. Know eˣ, sin x, cos x and 1/(1 − x), the radius and interval of convergence, and the alternating series and Lagrange error bounds.
More AP Calc BC practice
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