Věta (podílové kritérium).

• $$\lim_{n\to \infty} \frac{a_{n+1}}{a_n} < 1 \implies \sum_{n=1}^\infty a_n \text{ konverguje}$$
• $$\lim_{n\to \infty} \frac{a_{n+1}}{a_n} > 1 \implies \sum_{n=1}^\infty a_n \text{ diverguje}$$

Věta (odmocninové kritérium).

• $$\limsup_{n\to \infty} \sqrt[n]{{\left\lvert a_n\right\rvert}} < 1 \implies \sum_{n=1}^\infty a_n \text{ konverguje}$$
• $${\left(\exists_\infty n\right)} {\left(\sqrt[n]{{\left\lvert a_n\right\rvert}} > 1\right)} \implies \sum_{n=1}^\infty a_n \text{ diverguje}$$

Věta (Raabeovo kritérium).

• $${\left(\forall n\right)} {\left(n {\left(1 - \frac{a_{n+1}}{a_n}\right)} \le 1\right)} \implies \sum_{n=1}^\infty a_n \text{ diverguje}$$
• $$\lim_{n\to \infty} n {\left(1 - \frac{a_{n+1}}{a_n}\right)} > 1 \implies \sum_{n=1}^\infty a_n \text{ konverguje}$$

Věta (Gaussovo kritérium). $${\left(\exists q \in \R^+_0, \alpha \in \R, \varepsilon \in \R^+, c \in \R^\omega, c \text{ omezená}\right)} {\left(\frac{a_{n+1}}{a_n} = q + \frac{\alpha}{n} + \frac{c_n}{n^{1+\varepsilon}}\right)} \implies$$

• $$(q,\alpha) < (1,-1) \implies \sum_{n=1}^\infty a_n \text{ konverguje}$$
• $$(q,\alpha) \ge (1,-1) \implies \sum_{n=1}^\infty a_n \text{ diverguje}$$

Věta (srovnávací kritérium). Nechť $b$ je posloupnost s kladnými členy.

• $$\lim_{n\to \infty} \frac{a_n}{b_n} > 0 \land \sum_{n=1}^\infty b_n \text{ diverguje} \implies \sum_{n=1}^\infty a_n \text{ diverguje}$$ $$\lim_{n\to \infty} \frac{a_n}{b_n} < \infty \land \sum_{n=1}^\infty b_n \text{ konverguje} \implies \sum_{n=1}^\infty a_n \text{ konverguje}$$