# Math 122: Chapter 9 Exam Study Guide

- Determine whether the series converges absolutely, converges conditionally, or diverges. You do not need to show work. 14 parts.
- Find the summation. Look at telescoping and geometric series. Two parts.
- Write an expression for the n
^{th} term of the sequence with n starting at 1. Then determine the value to which the sequence converges. 3 parts.
- Find the radius and interval of convergence for the power series. Be sure to check the endpoints separately if necessary. 4 parts.
- Rewrite as a single power series. You may have some terms at the beginning that don't fit into the summation notation that need listed separately.
- The values for f
^{(k)}(0) for an unknown function are given. Use them to write a Maclaurin polynomial. Use the Maclaurin polynomial to estimate the value of the function at a particular point. Find the relative error in your approximation.
- Differentiate a power series in summation form.
- Integrate a power series in summation form.
- Write the first four non-zero terms (before writing the ...) in the power series expansion by making a substitution into a known Maclaurin series. 5 parts.

## Notes

- There are 108 possible points, but the exam is worth 100 points.
- You should bring paper for work. Write your answers on the exam itself.
- You will need the table of common Maclaurin series for the exam.

## Points per problem

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
Total |

Pts |
42 |
6 |
9 |
16 |
6 |
6 |
4 |
4 |
15 |
108 |