Cal2Test3

Front 1

p series 1/n to p power

Back 1

if p>1 con

if p<1 div

Front 2

basic comparison test

Back 2

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

Front 3

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

Back 3

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

Front 4

alternating series test

Back 4

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

Front 5

integral test

Back 5

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

Front 6

absolutely con

Back 6

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

Front 7

conditionally con

Back 7

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

Front 8

if sigma An is absolutely con

Back 8

then it is con

Front 9

ratio test

Back 9

the limit of An+1/An =L
L<1 then An series is absolutely con

L>1 or =infinity, then An series is divergent

Front 10

root test

Back 10

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

Front 11

power series

Back 11

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

Front 12

power series

Back 12

when -1<x<1 the series con

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

Front 13

root test used when

Back 13

An->Bn to the n power

Front 14

ratio test

Back 14

when constant is to the nth power or involves n!