calculus convergence tests (series & integrals)

p integral from 0 to #

converges if P<1

diverges if P≥1

p integral/series from # to infinity

converges if P>1

diverges if P≤1

comparison test

compare confusing series/integral to known divergent or convergent series/integral

if series < known convergent series then converges

if series > known divergent series then diverges

limit comparison test

a = series we wonder about

b = known convergent or divergent series

find lim of a/b approaching infinity

if it’s 0 and b converges then a converges

if it’s a value then a does what b does

if it’s infinity and b diverges then a diverges

ratio test

integral test requirements

integral test

if there is a continuous, positive, decreasing function that matches the rule generating the terms of our series, then the series and integral either BOTH converge or BOTH diverge