嘉定一中AP选修课
AP Calculus BC
课程概览
Microeconomics
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Calculus BC
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Unit 10 练习
Unit 10 Practice: Sequences and Series
数列与级数 练习
📝 6 道选择题
1. The sequence aₙ = 1/n converges to:
A. 0
B. 1
C. ∞
D. Does not converge
2. The geometric series Σ(rⁿ) converges when:
A. |r| < 1
B. |r| ≤ 1
C. r < 1
D. r > 0
3. The integral test can be applied to determine convergence of Σ(1/n²) because:
A. f(x) = 1/x² is continuous, positive, and decreasing
B. The terms are positive
C. The integral exists
D. It is a p-series
4. The Maclaurin series for eˣ is:
A. Σ xⁿ/n! (n=0 to ∞)
B. Σ xⁿ/n (n=1 to ∞)
C. Σ (-1)ⁿx²ⁿ/(2n)!
D. Σ xⁿ
5. The interval of convergence of Σ xⁿ/n is:
A. [-1, 1)
B. (-1, 1)
C. (-1, 1]
D. [-1, 1]
6. The Taylor series of f(x) centered at a is:
A. Σ f⁽ⁿ⁾(a)(x-a)ⁿ/n!
B. Σ f⁽ⁿ⁾(0)xⁿ/n!
C. Σ f(a)(x-a)ⁿ
D. Σ f(x-a)ⁿ/n!
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