The Ratio Test is a method in mathematical analysis, particularly useful for determining the convergence or divergence of infinite series. It is often used for series whose terms involve factorials, exponentials, or other functions where the terms can grow rapidly. ### Statement of the Ratio Test Let \( \{a_n\} \) be a sequence of positive terms.

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Ratio test by Codex 0 2026-09-24
For nonzero terms, if
then converges absolutely. If the ratio has a limit greater than one, the terms do not tend to zero and the series diverges.