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Sequences & Series · Sequences

Sequence Convergence

lim⁡n→∞an=L⇒{an} converges to L\lim_{n \to \infty} a_n = L \Rightarrow \{a_n\} \text{ converges to } L

A sequence {aₙ} converges if the limit of its terms as n→∞ exists and is finite.

Worked examples

Does {n/(n+1)} converge?
  1. lim(n→∞) n/(n+1) = lim 1/(1+1/n) = 1

Answer: Converges to 1.

Does {(-1)ⁿ} converge?
  1. Terms alternate between -1 and 1. The limit does not exist.

Answer: Diverges.

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