Their next objective is to find the hideout of a third agent, named Adam. Adam is very cautious. and never strays far from his hideout. Through careful observation, Angelina notices that Adam never leaves the street his hideout is on, and only travels east or west, leading her to conclude that Adam' 5 movements are confined to the interval of convergence of the following power series: J 00 (3)n(n-)3 xa 2n+1 Z ((372)!) ( l where a: is measured in miles east of the center of town, and a is the location of Adam's hideout. 11. a) What is the maximum distance Adam will travel from his hideout? b) If the furthest Adam ever travels east is 6 miles east of the center of town, Where is Adam's hideout located? c) Brad and Angelina are thinking of confronting Adam in the center of town. Compute the interval of convergence and determine if this is possible. 3 3n+1 I 3 (Hint: You may assume lim w 1km (3n)! dweryes. )