Convergence Tests

Here lists common Convergence Tests and overview of each. Details are singled out to each section.

Convergence test are a set of tests to determine wether the series CONVERGENT or DIVERGENT. It includes:

Test	Description
► Divergent Test	Take nth term's limit. (only to test divergence)
► Integral Test	Take limit of the series function's integration.
► p-series Test	Examine at the p value of 1/nᴾ.
► Comparison Test	Compare the series to a "similar" p-series or geometric-series.
► Ratio Test	Take limit of two terms ratio.
► Root Test	Take the limit of nth root of nth term.
► Alternating Test	Test if terms are decreasing, and take limit of nth term.

Divergent Test

Take the limit of nth term, if it's NOT ZERO, then it's DIVERGENT.

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Integral Test

p-series Test

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Direct Comparison Test

Compare the series to a "similar" p-series or geometric-series.

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Limit Comparison Test

Compare the series to a "similar" p-series or geometric-series.

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Ratio Test

Take limit of two terms ratio.

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Root Test

Take the limit of nth root of nth term.

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Alternating Series Test

Test if terms are decreasing, and take limit of nth term.

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Absolute Convergence & Conditional Convergence

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