Calculus Convergence Tests

when does the p-series test converge?

p>1
when does the p-series diverge?

0<p1
when can you use the p harmonic series? what happens to the series?
- 1/k p=1
- diverges
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 p-series
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
form for p-series
- {I} 1/k^p
- p>0
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
- lim ak/bk=L
- 0<L<infinity

Author

lacythecoolest

287525

Card Set

Calculus Convergence Tests

Description

Convergence Tests

Updated

2014-10-30T03:41:41Z

Show Answers