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15 Cards in this Set
- Front
- Back
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indeterminate forms
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0/0
inf/inf 0*inf 1^inf 0^0 inf-inf |
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special case of improper interval with integral of 1 to inf with dx/x^p
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take 1/p-1
converages if p>1 diverages if p<-1 |
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sum of geometric series
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a/(1-r)
where a is first term and r the multiple |
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in a geometric series if r><1
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abs r >- 1 , diverges
abs r between 0 and 1, converges (not including one) |
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nth term test
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take limit of the nth tern, limit from an, must be =0 to converge.
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integral test
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if fx is positive, continuous, decreasing, series will converge if integral converges and vice versa (both behave the same).
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p test
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for sum of 1/n^p
converges p>1 diverges is p is between o and 1 (including 1) |
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direct comparison
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appearances aside!
-if a bigger series converges, then the smaller one converges. -if a smaller one diverges, the bigger diverges. |
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limit comparison test
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(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. |
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alternating series test
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both alternating and non alternating converge if:
lim of positive is zero, and a+1n<an |
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absolute convergence
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means if abs a converges, then a also converges
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conditional convergence
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means sum an converges but abs an diverges
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ratio test
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an+1/an, take limit of abs.
converges if <1 diverges if >1 or lim = infinity INCONCLUSIVE if = 1 |
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If ratio test is inconclusive try moving to the
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alternating series test
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root test
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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. |
