A list of Important Series and Series Tests

Name of Test or Series Notes suggesting when to use the particular test
   
Geometric Series a series of a particular form:  sigma a rn 
Partial Fractions Series a series of a particular  form:   sigma 1((n-a)(n-b)) 
Divergence Test "limit of the terms not zero test" 
Harmonic Series a particular divergent series of the form:  sigma  1/n 
Integral Test useful when terms of series "have an antiderivative" 
P-Series a series of a particular form:  sigma 1/np 
Comparison Test last resort
Limit Comparison Test last resort
Alternating Series Test easily recognizable as having terms with alternating signs,  (-1)n
Ratio Test useful for terms containing factorials and powers
Root Test useful for terms containing powers
Theorems series of a sum, constant multiple, etc