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Lesson: Remainder of an Alternating Series Mathematics • Higher Education

In this lesson, we will learn how to find the error when approximating an alternating series by a finite term of the series.

Lesson Plan

Students will be able to

  • understand when we can approximate an alternating series by a finite term,
  • understand the accuracy of this approximation.

Lesson Video

Video Thumbnail
17:51

Lesson Worksheet

Q1:

Calculate the partial sum π‘†οŠ for the least 𝑛 terms that guarantees that the sum of the first 𝑛 terms of the alternating series βˆžοŠοŠ²οŠ§οŠοŠ°οŠ§οŠο„š(βˆ’1)5 differs from the infinite sum by 10 at most. Give your answer approximated to six decimal places.

Q2:

Calculate the partial sum π‘†οŠ for the least 𝑛 terms that guarantees that the sum of the first 𝑛 terms of the alternating series βˆžοŠοŠ²οŠ§οŠοŠ°οŠ§ο„š(βˆ’1)√2𝑛 differs from the infinite sum by 10 at most. Give your answer approximated to 3 decimal places.

Q3:

Consider the alternating series βˆžοŠοŠ²οŠ§οŠοŠ°οŠ§οŠ¨ο„š(βˆ’1)𝑛.

Find the value of the first 𝑛 that guarantees that the sum of the first 𝑛 terms of the series differs from the infinite sum by 10 at most.

Calculate the partial sum π‘†οŠ for the 𝑛 terms in the previous part. Give your answer to five decimal places.

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