Convergence Tests

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11 Terms

1
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nth term test

always start with this

<p>always start with this</p>
2
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Geometric Series

if it looks like a geometric series with a(r )n

<p>if it looks like a geometric series with a(r )<sup>n</sup></p>
3
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P-Series

if there is 1/np

<p>if there is 1/n<sup>p</sup></p>
4
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Alternating Series

if there is (-1)n

<p>if there is (-1)<sup>n</sup></p>
5
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Direct Comparison

if it looks VERY similar to another series you already know the convergence of (usually p-series, geometric series, alternating series)

<p>if it looks VERY similar to another series you already know the convergence of (usually p-series, geometric series, alternating series)</p>
6
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Limit Comparison

if you can still find a series you know the convergence of, but it’s too hard to prove an less than/greater than bn using Direct Comparison test (usually involves polynomials that you only look at the highest degrees of and can actually be used instead of DCT most of the time)

<p>if you can still find a series you know the convergence of, but it’s too hard to prove a<sub>n</sub> less than/greater than b<sub>n</sub> using Direct Comparison test (usually involves polynomials that you only look at the highest degrees of and can actually be used instead of DCT most of the time)</p>
7
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Absolute/Conditional Convergence

just use it if they ask you to determine absolute/conditional convergence

<p>just use it if they ask you to determine absolute/conditional convergence</p>
8
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Ratio Test

Factorials or exponentials

<p>Factorials or exponentials</p>
9
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Telescoping Series

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10
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Power Series

<p></p>
11
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Integral Test

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