Handouts on Sequences and Series for M 408D Spring 2024

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Click on the desired handout name.

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• Two Root Test Examples and Two Ratio Test Examples
• Alternating Series Examples
• The Level-of-Error Formula for a Convergent Alternating Series
• Explaining the Alternating Series Level-of-Error Formula
• The Comparison Test and The Limit Comparison Test
• The First Task in Applying the (Direct) Comparison Test and Limit Comparison Test and SUGGESTED WORDINGS of the Required Justifications for Each Test
• The Examples of Using the (Direct) Comparison Test Presented in Class
• The Example of Using the Limit Comparison Test Presented in Class
• Solutions to #38 and #39 of Section 11.3.
• Applying the Integral Test Correctly and the Suggested Wording for the Required Justification for the Integral Test
• Model Solutions Using P-Series and the Integral Test (From Edtion 8 of Stewart's Book "Calculus")
• Solutions to #9 and #38 of Section 11.3.

• Model Solutions for Two Problems: Worked Out Solutions for Section 11.3, Problems #40 and #41
• Solution to #28 of Section 11.4 proving that [ The Summation of (n + 3ⁿ) / (n + 2ⁿ) ] is Convergent
• The Remainder R_n for an infinite series from a Convergent Integral Test Application
• Why the Integral Test Works (when it applies)
• Lecture Notes for the First Lecture on Series
• First Notes on Series
• The Limit of a Sequence -- Definitions
• Correct to Three Decimal Places?
• How the Partial Sums s_n Approach Sum s When a Convergent Series has All Positive Terms
• Alternating Series Examples
• The Level-of-Error Formula for a Convergent Alternating Series
• Explaining the Alternating Series Level-of-Error Formula
• Three Important Principles