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Calculus (42)
Midterm

# Summary and Strategies for Convergent Tests.docx

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School
Western University
Department
Calculus
Course
Calculus 1301A/B
Professor
Natalia Kiriushcheva
Semester
Winter

Description
Summary and Strategies for Convergent Tests Type Strategy Condition for Convergency Sequences (function) a n Converges at existing limit (each term approaches it) r |r| < 1 Sum Sn Converges at existing limit (sum of series = limit) Telescoping Converges at existing limit Geometric n n-1 Series ∑ r = (r)r |r| < 1 converging at Harmonic ∑ Diverges Series -p P Series ∑ n = p > 1 converging at General ∑ ≠ 0  divergent = 0  inconclusive, use the following tests ∫ Positive and decreasing at [a,∞)  Integral (easy to integrate) Finite number ≤ b  Comparison n If n converges through other tests, then converges ≥ bn If n diverges through other tests, then diverges positive series If test fails, use limit comparison  Limit Comparison L > 0 (since series always positive, L > 0) Alternating ∑ = 0 Series cos(n)  (-1) an+1< an(decreasing)  Harmonic Series Conv
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