This lesson introduces the topic of limits of sequences. Right away I demonstrate the first, fundamental technique for computing those limits — factoring out the highest power.

From it you will learn, among other things, how to grasp in a simple way what the limits of sequences are and how helpful that understanding is when computing them.

You will also become familiar with two fundamental, elementary limit formulas—used at virtually every turn—whose very existence many beginners are unaware of when they start learning.

This lesson lasts 75 minutes and contains 30 step-by-step examples, including examples with exponential expressions and factorials.

Table of Contents:

• Intuitive overview of the limit of a sequence and its formal definition [02:26]
• Sequences – 5 examples [12:22]
• Indeterminate forms [22:53]
• Factoring out the highest power – examples 1-3 [25:50]
• Factoring out the highest power – examples 4-8 [34:03]
• Factoring out the highest power – examples 9-12 [42:10]
• Factoring out the highest power – examples 13-16 [47:30]
• Factoring out the highest power – examples 17-18 [52:15]
• Factoring out the highest power – examples 19-20 [57:37]
• Factoring out the highest power in exponential functions – 3 examples [01:00:51]
• Factoring out the highest power in factorial examples – example 1 [01:08:07]
• Factoring out the highest power in factorial examples – example 2 [01:11:07]

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Formulas needed for the Lesson

Download limit formulas (PDF)

Download trigonometric tables (PDF)

Homework

Download Homework (PDF)

Download Answers to Homework (PDF)

Articles and blog posts related to this Lesson

• “Limit of a sequence – intuitive introduction and definition”
• “Limit of a sequence from the definition – examples”
• “Indeterminate forms in limits of sequences”
• “Improper limit of a sequence”
• “Logarithm in a sequence limit – how to do it effortlessly? (VIDEO)”
• “Troubles with indeterminate symbols”
• “The symbol 0 in limits of functions and sequences“
• “Limit of a sequence with logarithms“