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Use the Divergence Criterion to prove that the sequence an = (−1)n + 1 n diverges.

Use the Divergence Criterion to prove that the sequence an = (−1)n + 1 n diverges.

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Answer #1

Theorem 1 (Divergence Criteria for Sequences):

A sequence (an) of real numbers is divergent if either one of the following hold:
1. (an) has two subsequences (an(k)) and (an(p)) that converge to two different limits.
2. (an) has a subsequence that is divergent.
3. (an) is unbounded.

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