CalcRef

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.

  • 2 worked examples
  • 18 in Sequences & Series

Worked examples

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

Answer: Converges to 1.

1 more worked examplePremium

Does {(-1)ⁿ} converge?

Step-by-step solution locked.

Unlock the full working. CalcRef Premium opens the step-by-step solution above, and 141 worked solutions across the whole library - the intermediate lines, not just the answer. The formula statement, its conditions, its variables and the first worked example stay free on every page.
See PremiumBrowse the free reference

See all 18 Sequences & Series formulas on one printable sheet - the same statements and conditions as these pages, typeset and laid out for paper.

Common questions

What is the Sequence Convergence?

A sequence {aₙ} converges if the limit of its terms as n→∞ exists and is finite. It is one of the sequences & series formulas in the CalcRef reference.

How do you use the Sequence Convergence?

Worked example. Does {n/(n+1)} converge? lim(n→∞) n/(n+1) = lim 1/(1+1/n) = 1. Answer: Converges to 1.

Practice

Quiz yourself on Sequences & Series

Sequence Convergence is one of 18 Sequences & Series formulas in CalcRef, out of 136 in the library. Today's free round is 10 mixed multiple-choice questions drawn from the same dataset as this page, refreshed every day and replayable as often as you like - no account needed.

Take today's free quizAll 18 Sequences & Series formulas