# 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. Differentiate a power series in summation form and leave the answer in summation form.
7. 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.
8. Use a known Maclaurin series to write the first four non-zero terms in the series expansion. 6 parts.
9. Integrate a power series in summation form. Then use it to find an approximation accurate to the specified tolerance.

## Notes

• You should bring paper for work. Write your answers on the exam itself.
• You may use a table of common Maclaurin series during the exam.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 Total 28 6 9 16 5 5 8 18 5 100