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.
Integral Test
p-series Test
Direct Comparison Test
Compare the series to a "similar" p-series or geometric-series.
Limit 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 Series Test
Test if terms are decreasing, and take limit of nth term.
Absolute Convergence & Conditional Convergence
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