Tests for series divergence

Test for divergence by sequence limit

The test for divergence is based on the observation that if the limit of a sequence is not , the corresponding series must diverge.

Clearly, if , then for sufficiently large the series is approximated by the trivially divergent .

Note that the implication only goes one way. A sequence term limit of is not sufficient to show a series converges. For example, the harmonic series does not converge.

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