Created by: Josh Carlson
Tests for Sequences and Series
Ch. 9.1: Sequences
Squeeze Theorem: Flags: Sin/Cos
,
Monotonic Sequence Theorem: Flags: n! or an
[
[
]
Note: Non-Increasing means
]
, and Non-Decreasing means
Theorem C:
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Ch. 9.2: Series
Sequence of Partial Sums:
∑
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Nth term test for divergence:
∑
Geometric Series:
∑
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Harmonic Series:
∑
Collapsing Series: Flags: iteration/subtraction
Writing out the sequence of partial sums (Sn) will produce cancellations that allow us to get a
formula for the sequence. We can use Sn to tell convergence or divergence of the series.
Created by: Josh Carlson
Ch 9.3: Positive Series
Integral test: Flags: Can you integrate it?
∫
∑
P-Series Test:
∑
Bounded Sum Test:
∑
Ch 9.4: Positive Series Continued
Ordinary Comparison Test:
Limit Comparison Test: Flags: polynomial/polynomial Ratio Test: Flags: n! or an


.
Ch 9.5: Alternating Series
Absolute Ratio Test: Flags: n! or a
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
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n
Definitions:
If | | converges we say
Converges Absolutely.
If | | converges but
diverges we say
Conditionally Convergent.
Alternating Series Test:
∑
Absolute Convergence Test:
If a series converges absolutely then it converges.
is