Eight sentences**Below you will find two topics. Using only one of the topics, post at least three things you notice and one thing you wonder or are curious about.You should include in your response your mathematical analysis using any vocabulary and content from the chapter. Be insightful and in depth,with your responses. Not everything you wonder about should be "I wonder how this is used in real life." Also, please don't post, "there is really nothing I wonder about " or any variation of that statement.

THEOREM 6.1 Convergence of a Power Series Consider the power series 2 on (m a)". 11:0 The series satisfies exactly one of the following properties: i. The series converges at a: = a. and diverges for al! m =, a. ii. The series converges for all real numbers x. iii. There exists a real number R > 0 such that the series converges if la: a] R. At the valuesx where [3: cl = R, the series may converge or diverge. THEOREM 6.2 Combining Power Series Suppose that the two power series 2: CH 2:" n=0 and Z d" 9:" converge to the functions r' and n=0 9, respectively, on a common interval 1. CK: i. The power series 2 (cnz" i dam\") n=0 converges to f :t g on 1. ii. For any integer m 2 0 and any real number b. the power series 2: b:r:"'c.1 1:" converges to (1sz (:5) on I. iii. For any integer m > 0ac and any real number b. the series n: c,.(b:1:"')n converges to f (bzm) for all x such that be\" is in