嘉定一中AP选修课
AP Calculus BC
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Microeconomics
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Assignment 13: Series Convergence
Assignment 13: Series Convergence
级数收敛性综合练习
综合练习:收敛判别法、绝对/条件收敛
✍️ 5 题
1. Which test is best for Σ n!/(nⁿ)?
A. Ratio Test
B. Integral Test
C. Comparison Test
D. Root Test
2. Σ (-1)ⁿ/√n is:
A. Conditionally convergent
B. Absolutely convergent
C. Divergent
D. Cannot determine
3. By the Integral Test, Σ 1/(n²+1) converges because:
A. ∫₁∞ dx/(x²+1) converges
B. The terms go to zero
C. It is a p-series with p>1
D. By comparison with 1/n
4. If Σ aₙ converges absolutely, then:
A. Σ aₙ converges
B. Σ aₙ might diverge
C. Σ |aₙ| diverges
D. The terms do not approach zero
5. Use the Limit Comparison Test with bₙ = 1/n³ to determine if Σ n/(n⁴+1) converges:
A. Converges (limit = 1, Σ 1/n³ converges)
B. Diverges
C. Inconclusive
D. Converges conditionally
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