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Seq/Ser Test One
Series types, convergence conditions
8
Mathematics
Undergraduate 1
09/26/2008
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Term
Harmonic Series
 Definition

infinity        

 [image] (1/n)

 n=1        

Term

Harmonic Series

converge or diverge?

Definition
Diverges
Term
Geometric Series
 Definition

infinity       

[image]ar^n

n=0       

Term

Geometric Series

converge or diverge?

Definition

0<r<1 , converges with

 

 a

------

1-r

Term
P-Series
 Definition

 infinity         

[image]1/n^p

n=1        

Term

P-Series

converge or diverge?

Definition

p</=1, diverges

p>1, converges

Term
Alternating Series
 Definition

infinity                 

[image](-1)^n (1/n)

n=1                 

Term

Alternating Series

converge or diverge?

Definition
converges IF AND ONLY IF |terms| descend to 0
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