# Math 122: Chapter 9 Exam Study Guide

1. Determine whether the series converges absolutely, converges conditionally, or diverges. You do not need to show work. 14 parts.
2. Find the summation. Look at telescoping and geometric series. Two parts.
3. Write an expression for the nth term of the sequence with n starting at 1. Then determine the value to which the sequence converges. 3 parts.
4. Find the radius and interval of convergence for the power series. Be sure to check the endpoints separately if necessary. 4 parts.
5. 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.
6. 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.
7. Differentiate a power series in summation form.
8. Integrate a power series in summation form.
9. 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

 # Pts 1 2 3 4 5 6 7 8 9 Total 42 6 9 16 6 6 4 4 15 108