# Math 172 : Midterm 3

Thursday 11/14 @ 6-7:50pm

 Summary Points: 1) Exam Topics  Geometric and Telescoping Series                                              (section 10.2) Divergence Test                                                                       (section 10.2) Integral Test and p-series                                                         (section 10.3) Comparison and Limit Comparison Tests                                    (section 10.3) Alternating Series Test and Error Bounds                                   (section 10.4) Absolute and Conditional Convergence                                      (section 10.4) Ratio and Root Tests                                                                (section 10.5) Power Series and radius/interval of convergence                        (section 10.6) Taylor series expansion (Theorem 1, pg 592).                            (section 10.7) Shortcuts for Taylor series (pg 594-597) and limits                     (section 10.7) The exam topics are different than your previous calculus topics. For one, there is a fair amount of memorization. Also, calculations are minimal generally speaking. The exam will reflect both of these facts. Make sure you know the theorems and definitions! 2) There is no question specifically on the sequence material in section 10.1. However, you will be required to take limits of sequences {an} when using tests like the Ratio and Root tests. 3) Unless otherwise stated you must verify all test hypotheses for full credit as in Comparison tests, Integral test, alternating series test etc. A summary of these tests is here. You will be required (at some point) to state all the hypotheses and conclusions of a convergence test as well. 4) There will be a 10 point true false question like these or at the end of this. 5) Miscellaneous remarks: A formula sheet will be provided for Taylor Series -  formula sheet below If you use L'Hospital's rule one must take the limit of the associated real function, i.e. f(x)=sin(x)/x versus sin(n)/n. Failure could cost a point. Same applies when using the integral test, i.e., you can integrate f(x)=ln(x)/x but not the sequence an=ln(n)/n. Many exam questions are minor variants of homework problems. Generally speaking the HW is a good guide to the kinds of problems on the test. You should be able to do the exam in 60-75min but will have 1hr and 50min 6) Remember our tutoring resources - both the Math Learning Center and review sessions held by Corinne Casolara (SSC).

Formula Sheet that will be attached to Midterm:

TECBL - Technology Enhanced Criteria Based Learning