AP Calc BC 10A Test

geometric series formula

a(r)ⁿ

what can you determine from geometric series?

if 0<|r|<1, series converges

what can you determine from the nth term test?

if the limit of a series is not equal to 0, it diverges

if it does, the convergence or divergence is inconclusive

integral test conditions

positive, continuous, and decreasing

what can you tell from the integral test?

if the integral of a function converges, the sum also converges

same for divergence

p-series formula

1/n^p

what can you tell from a p-series test?

if p>1, it converges

if 0<p≤1, it diverges

how can you determine divergence with the direct comparison test?

when a_n<b_n, if a_n diverges, b_n also diverges

how can you determine convergence with the direct comparison test?

when a_n<b_n, if b_n converges, a_n also converges

what can you determine from the limit comparison test?

if the limit of (a_n/b_n) = L, where L is finite and positive, both series either converge or diverge

alternating series formula

(-1)ⁿ*a_n

conditions for alternating series test

lim of function is 0, must be non-increasing

what can you determine from the ratio test?

if |a_n+t/a_n|<1, series converges

if |a_n+t/a_n|>1 or is infinity, diverges

if |a_n+t/a_n|=1, inconclusive

what can you determine from the root test?

if the limit of |a_n|^1/n<1, converges absolutely

if the limit of |a_n|^1/n>1 or is infinity, diverges

if the limit of |a_n|^1/n=1, inconclusive

how can you determine if a converging alternating series is absolutely converging or conditionally converging?

if the limit of |a_n| also converges, it is absolute. if not, it is conditional

how to determine error of an alternating series?

it is less than or equal to the abs value of the next term