[AP Calc] Unit 9: Series and Sequences
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16 Terms
1
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partial sum
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geometric series
|r|
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harmonic series
always divergent
4
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test for divergence
if the lim(a) DNE or lim(a)≠0 → the series is divergent
5
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integral test
only used if the function is continuous, positive, and decreasing
take the integral, then the limit
take the integral, then the limit
6
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p-series
p>1; convergent
p≤1; divergent
p≤1; divergent
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remainder estimate for the integral test
where is f continuous, positive, and decreasing for x≥n and Σa is convergent
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comparison test
if Σa and Σb are series with positive terms
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limit comparison test
where c is positive and finite and Σa and Σb are series with positive terms
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alternating series
a series whose terms alternate from positive to negative
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alternating series test
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alternating series error bound theorem
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absolutely convergent
a series, Σa, is ______ if Σ|a| is convergent
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conditionally convergent
a series, Σa, is ______ if Σ|a| is divergent
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ratio test
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root test
