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 CONVERGENTor DIVERGENT.
It includes:

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