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A list of Important Sequences and Sequence Tests |
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| Name of Test or Sequence | Notes suggesting when to use the particular test |
| Connect the Dots | Change the integer variable n to a real variable x and use the methods of the chapter on limits at infinity to find the limit of the sequence. |
| Connect the Dots and use l'Hopital's rule | Change the integer variable n to a real variable x and use l'Hopital's rule to find the limit of the sequence. |
| Geometric Sequence | a sequence of a particular form: a rn |
| P-Sequence | a sequence of a particular form: 1/np |
| Recursively Defined Sequences | Each term is defined in terms of the one(s) before rather than in terms of n alone. |
| Arithmetic Theorems | Sum, product, constant multiple, etc. |
| Squeeze Theorem (Sandwich Thoerem) | |
| Absolute Value to Zero Theorem | |
| Bounded Monotonic Theorem | |