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14 Cards in this Set

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  • 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 n-1 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 x-a <R and diverges if abs value of x-a >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!