Lesson: Remainder of an Alternating Series AP Calculus BC

Mathematics

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

Video

17:51

Sample Question Videos

  • 09:48
  • 05:22
  • 04:46

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:

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.

Q3:

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

Find the value of 𝑛 that guarantees that the sum of the first 𝑛 terms of the series differs from the infinite sum by 10οŠͺ 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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