MATH 6B–Winter 2016Vector Calculus IIStudy Guide Midterm 2: Extra Problems1. Recognize a geometric series. In the following examples, give a check mark to the geometric series andtwo check marks to the convergent geometric series. Find their sum when possible. If the series is notgeometric, can you determine their convergence/divergence?
2. Identify what is the optimal test to determine convergence of a series. For the following series, write atleast one test that will determine their convergence/divergence, describe how you will use each test, andstate the reason why the test applies.(a)∞Xn=1n!2nRatio Test
→∞2n+1n!2n= limn→∞(b)∞Xn=11n3+ 1Limit Comparison Test