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Calculus 2 (Special Ed course)
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Q1: The ratio test for series Σ a, if lim |a,+1/a | = L then the series ___
Converges if L < 1, diverges if L > 1, inconclusive if L = 1
Diverges if L < 1
Converges if L > 1
Always converges
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Q2: Which test would you FIRST try for Σ (1/n²)?
Integral test
p-series test
Ratio test
Comparison test
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Q3: Fill in the blank: The interval of convergence for Σ x^n/n from n=1 to ∞ is
(-1,1)
[-1,1)
(-1,1]
[1,1]
Q4: TRUE or FALSE: The harmonic series Σ 1/(1/n) diverges even though its terms approach zero.
True
False
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Q5: Does the series Σ 1/(n²) from n=1 to ∞ converge or diverge?
Diverges - harmonic series
Converges - p-series with p=2 > 1
Converges - ratio test gives 0
Diverges - terms don't approach zero
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Correct Ratio test: L < 1 converges, L > 1 diverges (fails tests, try another)
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Correct ratio test works best when factorials or exponentials are present. Σ(1/n²) = Σ(1/n²) (n²+2n+1)/n² = Σ(n²+2n+1)/n⁴
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Correct: The interval of convergence for Σ x^n/n is (-1, 1].
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Correct: The harmonic series diverges.
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Correct: The series Σ 1/n² converges because it is a p-series with p=2 > 1.
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