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MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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13.4 Limits at Infinity; Limits of Sequences

Focus on sequence limit and sequence convergence.

Before you solve

Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Limits at infinity of rational functionsWorked steps · five questions02Limits of sequencesWorked steps · five questions
Lesson brief and rules

13.4 Limits at Infinity; Limits of Sequences

For positive integer n,1nn, \frac{1}{n} approaches 00 as nn grows without bound.

Worked example 11
01 / Find lim⁡n→∞(4+1n)\displaystyle \lim n\to \infty (4+\dfrac{1}{n}).
02 / 1n\dfrac{1}{n} tends to 00 as nn grows, so the limit is 44.
03 / Answer: 44
Worked example 2 · Sequence convergence

Does an=1na_{n}=\dfrac{1}{n} converge?

1n\dfrac{1}{n} tends to 00 as nn grows. Answer: Yes, to 00

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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