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Calculus Convergence Tests
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when does the p-series test converge?
p>1
when does the p-series diverge?
0<p
1
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
ID
287525
Card Set
Calculus Convergence Tests
Description
Convergence Tests
Updated
2014-10-30T03:41:41Z
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