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Ratio Test

The Ratio Test measures the rate of growth (or decline) of a series by examining the ratio $\frac{a_{n+1}}{a_n}$

Ratio Test - Theorem

Leg $\sum a_n$ be a series with positive terms, and suppose that $$\lim_{n \to \infty} \frac{a_{n+1}}{a_n} = p$$ Then:
  1. The series _converges_ if $p < 1$
  2. The series _diverges_ if $p > 1$ or is infinite
  3. The test is _inconclusive_ if $p = 1$




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Content source: tommytwoeyes/continuity

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