嘉定一中AP选修课
AP Calculus BC
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Microeconomics
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Assignment 12: Power Series
Assignment 12: Power Series
幂级数
幂级数相关练习：收敛半径、幂级数表示
✍️ 5 题
1. Find the radius of convergence of Σ (xⁿ)/n from n=1 to ∞
A. R = 1
B. R = ∞
C. R = 0
D. R = e
2. The power series Σ n·xⁿ from n=1 to ∞ converges for:
A. |x| < 1
B. All x
C. x = 0 only
D. |x| ≤ 1
3. Find the interval of convergence for Σ (x-2)ⁿ/n²
A. [1, 3]
B. (1, 3)
C. [0, 4]
D. All x
4. Differentiate the power series Σ (xⁿ/n!) term by term. The result is:
A. Σ (xⁿ⁻¹/(n-1)!) from n=1 to ∞
B. Σ (n·xⁿ⁻¹/n!)
C. Σ (xⁿ/(n+1)!)
D. The same series
5. The series 1 + x + x² + x³ + ... equals (for |x|<1):
A. 1/(1-x)
B. 1/(1+x)
C. 1+x
D. Does not converge
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