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Sequences & Series · Convergence Tests

Divergence Test

lim⁡n→∞an≠0⇒∑an diverges\lim_{n \to \infty} a_n \neq 0 \Rightarrow \sum a_n \text{ diverges}

If the terms do not approach zero, the series diverges. CAUTION: If the limit IS zero, the test is inconclusive (the series may still diverge).

  • 0 variables
  • 2 worked examples
  • 18 in Sequences & Series

Worked examples

Does Σ n/(2n+1) converge?
  1. lim(n→∞) n/(2n+1) = 1/2 ≠ 0

Answer: Diverges by the divergence test.

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Can the divergence test determine if Σ 1/n converges?

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