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Root Test

For more complicated patterns in infinite series (see the example below), other convergence/divergence tests may not suffice.

For certain patterns in series, the Root Test may work better.

Root Test

Let $\sum a_n$ be a series with $a_n \ge 0$ for $n \ge N$, and suppose that: $$\lim_{n \to \infty} \sqrt[n]{a_n} = p$$ Then the series:
  1. _converges_ if $p < 1$
  2. _diverges_ if $p > 1$ or $p \to \infty$
  3. has an _inconclusive_ result if $p = 1$




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Content source: tommytwoeyes/continuity

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