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15 Cards in this Set

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indeterminate forms
0/0
inf/inf
0*inf
1^inf
0^0
inf-inf
special case of improper interval with integral of 1 to inf with dx/x^p
take 1/p-1
converages if p>1
diverages if p<-1
sum of geometric series
a/(1-r)
where a is first term and r the multiple
in a geometric series if r><1
abs r >- 1 , diverges
abs r between 0 and 1, converges (not including one)
nth term test
take limit of the nth tern, limit from an, must be =0 to converge.
integral test
if fx is positive, continuous, decreasing, series will converge if integral converges and vice versa (both behave the same).
p test
for sum of 1/n^p
converges p>1
diverges is p is between o and 1 (including 1)
direct comparison
appearances aside!
-if a bigger series converges, then the smaller one converges.

-if a smaller one diverges, the bigger diverges.
limit comparison test
(another way to do comparisons when the direct comparison test wont work)
limit as n goes to inf of an/bn (where a<b
if answer is FINITE and POSITivE, both converge or both diverge.
alternating series test
both alternating and non alternating converge if:
lim of positive is zero, and a+1n<an
absolute convergence
means if abs a converges, then a also converges
conditional convergence
means sum an converges but abs an diverges
ratio test
an+1/an, take limit of abs.
converges if <1
diverges if >1 or lim = infinity
INCONCLUSIVE if = 1
If ratio test is inconclusive try moving to the
alternating series test
root test
an converes absolutely if limit rt n (an)<1 , diverges if = infinity

INCONCLUSIVE if = 1

when applying the rrot just divide each exponent by N.