# Worksheet: Remainder of an Alternating Series

In this worksheet, we will practice finding the error when approximating an alternating series by a finite term of the series.

**Q1: **

Calculate the partial sum for the least terms that guarantees that the sum of the first terms of the alternating series differs from the infinite sum by at most. Give your answer approximated to six decimal places.

**Q2: **

Consider the alternating series .

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

Calculate the partial sum for the terms in the previous part. Give your answer to five decimal places.

**Q3: **

Consider the alternating series .

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

Calculate the partial sum for the terms in the previous part. Give your answer to five decimal places.

**Q4: **

For the alternating series , find the error bound when approximating the series by the first 20 terms. Give your answer to five decimal places.

**Q5: **

Calculate the partial sum for the least terms that guarantees that the sum of the first terms of the alternating series differs from the infinite sum by at most. Give your answer approximated to 3 decimal places.

**Q6: **

Is it possible to approximate the series by summing its first terms? If yes, find the value of the first that guarantees that the sum of the first terms of the series differs from the infinite sum by at most 0.4.

- AYes, .
- BYes, .
- CYes, .
- DYes, .
- ENo, the series diverges, so we cannot find an infinite sum to it.

**Q7: **

Which of the following series has a lower-bound error when approximated by the sum of its first 30 terms?

- A
- B
- C
- D
- E

**Q8: **

Which of the following series requires summing the least number of terms so that the finite sum differs from the infinite sum by at most ?

- A
- B
- C
- D
- E

**Q9: **

Find the maximum error bound when approximating the series by summing the first 20 terms. Round your answer to 5 decimal places.

**Q10: **

Find the lowest value of that guarantees that the sum of the first terms of the series differs from the infinite sum by 0.26 at the most.

- A
- B
- C
- D
- E

**Q11: **

Find the lowest value of that guarantees that the partial sum of the series differs from the infinite sum by at the most.

**Q13: **

Find the lowest value of that guarantees that the partial sum of the series differs from the infinite sum by at most .

**Q14: **

Which of the following series has a lower-bound error when approximated by the sum of its first 6 terms?

- A
- B
- C
- D
- E