Tests for series divergence

Comparison test

The comparison test for divergence of infinite series is analogous to the Squeeze Theorem. It states that if sequences and obey the relationship

for all , then the series obey the relation

and therefore the convergence of the latter series implies the convergence of the former, and the divergence of the former series implies the divergence of the former.

Often a series will be compared with a 𝑝-series.

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