Calculus Convergence Tests
Home > Flashcards > Print Preview
The flashcards below were created by user
lacythecoolest
on
FreezingBlue Flashcards. What would you like to do?

when does the pseries test converge?
p>1

when does the pseries diverge?
0<p
1

when can you use the p harmonic series? what happens to the series?

When does a ratio test converge?
L<1

when does a ratio test diverge?
L>1

what happens if L=1 on a ratio test?
no conclusion can be drawn

DCT first test
what needs to happen in order for b_k and a_k to converge
b_k converges and a_k<=b_k

DCT first test
what needs to happen in order for b & a _k to diverge
b_k diverges and ak>=bk

what are the only two allowable combinations of comparison series for the DCT
geometric series and pseries

conditions for the LCT
ak and bk are series with positive terms

procedure for LCT
take limit ak/bk=L

what does 0<L<inifinity tell you in a LCT
both series converge or both diverge

procedures for Ratio Test
 ak>0 for all k
 lim: ak+1/ak=L


conditions for the integral test
 f(x) is continuous, positive, and decreasing on interval [1, infinity)
 f(x)=ak

convergence/divergence on the Integral Test
 Antiderive ak
 ~either both converge or both diverge

conditions for Limit Comparison Test
ak and bk positive series

how does LCT converge and/or diverge