Convergence Tests
Last updated
Last updated
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.
Take the limit of nth term, if it's NOT ZERO, then it's DIVERGENT.
Compare the series to a "similar" p-series or geometric-series.
Compare the series to a "similar" p-series or geometric-series.
Take limit of two terms ratio.
Take the limit of nth root of nth term.
Test if terms are decreasing, and take limit of nth term.
