BC calc series rules

nth term test

(only for divergence, no convergence)

nth term test divergance

geometric series

geometric convergence

geometric divergence

sum of geometric series (where the series CONVERGES to)

direct comparison test

direct comparison convergence

direct comparison divergence

limit comparison test

limit comparison convergence

limit comparison divergence

limit comparison convergence FOR L= 0 and ∞

p-series test

p-series convergence

p-series divergence

alternating series test

alternating series convergence

Ex. Find error bound for an estimation made with the first 3 terms —> bound is defined as (a4)

Bound is always one greater than term

Alternating series error bound

function must be continuous, positive, and decreasing

integral test

integral convergence

integral divergence

ratio test convergence

ratio test divergence

ratio test =1 RULE