Relationship to Sequences of Absolute Values

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The following theorem can be used to evaluate limits of sequences when the sign of the terms in the sequence alternate between positive and negative.

Theorem: Relationship to Sequences of Absolute Values

The limit

equals zero if and only if

In other words, if we are given the sequence

and

then

The converse is also true but we will not use it. For us, this theorem is only useful as a test for convergence.


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Next: Example Relating Sequences of Absolute Values



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