Difference between revisions of "Ratio test"
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| − | <strong>Proof:</strong> █ | + | <strong>Proof:</strong> █ <br /> |
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| + | ==References== | ||
| + | [https://proofwiki.org/wiki/Ratio_Test] | ||
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Latest revision as of 18:38, 1 December 2015
Theorem: (The ratio test) Let $\{a_1,a_2,\ldots\} \subset \mathbb{C}$ and consider the infinite series $\displaystyle\sum_{k=0}^{\infty} a_k.$ Define $$L=\displaystyle\lim_{k \rightarrow \infty} \left| \dfrac{a_{k+1}}{a_k} \right|.$$
- If $L<1$, then the series converges absolutely,
- if $L>1$, then the series diverges,
- if $L=1$, then the test is inconclusive.
