Please write out as much as possible, due to I'm trying to learn this from the book. I do have the answer but i want to learn the process of it. Please do not USE CHEGGz, since i know course hero tutor are honest and do their own work.

Let 22:0 c,,(+8)\" be a power series that converges when a: = 0 and diverges when .1: = 3. (21) Using only the information provided, what is the smallest possible interval of con- vergence. Clearly indicate the inclusion or exclusion of each endpoint in the inter- val of convergence. (Hint: it might be useful to draw a number line.) (b) Using only the information provided, what is the largest possible interval of con- vergence. Clearly indicate the inclusion or exclusion of each endpoint in the inter- val of convergence. (Hint: it might still be useful to draw a number line.) (c) For each of the following, determine if the sum must converge, must diverge, or if there is not enough information. Fill in the table accordingly. No justication is required. Series Must Converge Not Enough Info 2:020 91112\" 2:020 Cn(_9)n 2:10 6,,(m + 8)\" for a: = 15