Calculus Convergence Tests

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

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