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15 Cards in this Set
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 Back
indeterminate forms

0/0
inf/inf 0*inf 1^inf 0^0 infinf 

special case of improper interval with integral of 1 to inf with dx/x^p

take 1/p1
converages if p>1 diverages if p<1 

sum of geometric series

a/(1r)
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. 