Study Guides
(238,491)

Canada
(115,165)

Western University
(11,891)

Calculus
(42)

Calculus 1301A/B
(7)

Midterm

# Summary and Strategies for Convergent Tests.docx

Unlock Document

Western University

Calculus

Calculus 1301A/B

Natalia Kiriushcheva

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

More
Less
Related notes for Calculus 1301A/B