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14 Cards in this Set
 Front
 Back
p series 1/n to p power

if p>1 con
if p<1 div 

basic comparison test

sum of Bn con AND An is less than or equal to Bn then An con
sum of Bn div AND An is greater than or equal to Bn then An div 

limit comparision test if An is given and Bn is reference series

limit of An/Bn=C and C>0, then both series con or both div
limit An/Bn=0 and sum of Bn con, then An con limt of An/Bn= infinity and sum of Bn div, then An div 

alternating series test

sum of 1 to n1 power as 1 to infinity is an alternating series
if limit of An =0 AND An+1 < An for all n, then the given series converges another way to show decreasing, f'x <0 

integral test

if f is cont., +, decreasing function on [1,infinity) then if the sigma series is con iff the improper integral is con.
therefore if integral is con, then the sigma series is con. if integral is div, then sigma is div 

absolutely con

if series of abs values sigma An is con, then it is called absolutely con


conditionally con

if the sigma An is con, but is not absolutely con.


if sigma An is absolutely con

then it is con


ratio test

the limit of An+1/An =L
L<1 then An series is absolutely con L>1 or =infinity, then An series is divergent 

root test

nth root of abs value of An =L
L <1 then series of An is absolutely con L>1, then the series of An is div 

power series

series converges only when x=a
series converges for all x there is a + # R such that the series converges if abs value of xa <R and diverges if abs value of xa >R 

power series

when 1<x<1 the series con
when abs value of x is > or = to 1, the series is div 

root test used when

An>Bn to the n power


ratio test

when constant is to the nth power or involves n!
