# Calculus Convergence Tests

### Card Set Information

 Author: lacythecoolest ID: 287525 Filename: Calculus Convergence Tests Updated: 2014-10-29 23:41:41 Tags: convergence calculus seriestest serie series tests Folders: Description: Convergence Tests Show Answers:

Home > Flashcards > Print Preview

The flashcards below were created by user lacythecoolest on FreezingBlue Flashcards. What would you like to do?

1. when does the p-series test converge?
p>1
2. when does the p-series diverge?
0<p1
3. when can you use the p harmonic series? what happens to the series?
• 1/k p=1
• diverges
4. When does a ratio test converge?
L<1
5. when does a ratio test diverge?
L>1
6. what happens if L=1 on a ratio test?
no conclusion can be drawn
7. 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
8. DCT first test

what needs to happen in order for b & a _k to diverge
b_k diverges and ak>=bk
9. what are the only two allowable combinations of comparison series for the DCT
geometric series and p-series
10. conditions for the LCT
ak and bk are series with positive terms
11. procedure for LCT
take limit ak/bk=L
12. what does 0<L<inifinity tell you in a LCT
both series converge or both diverge
13. procedures for Ratio Test
• ak>0 for all k
• lim: ak+1/ak=L
14. form for p-series
• {I} 1/k^p
• p>0
15. conditions for the integral test
• f(x) is continuous, positive, and decreasing on interval [1, infinity)
• f(x)=ak
16. convergence/divergence on the Integral Test
• Antiderive ak
• ~either both converge or both diverge
17. conditions for Limit Comparison Test
ak and bk positive series
18. how does LCT converge and/or diverge
• lim ak/bk=L
• 0<L<infinity

What would you like to do?

Home > Flashcards > Print Preview