$latex \mathbf{Question:} (a) \text{ Suppose that the sequence} \{c_k\} \text{is bounded. then the radius of } \\ \text{ convergence of } \sum_{k \geq 0}c_k(z-z_0)^k \text{is at least 1 }\\
(b) \text{ Suppose that the sequence } \{c_k\} \text{ does not converge to 0. then the radius of }\\ \text{ convergence of } \sum_{k \geq 0}c_k(z-z_0)^k \text{is at most 1. Then }\\ \\
\text{1. (a) is correct and (b) correct }\\
\text{2. (a) is wrong but (b) is correct}\\
\text{3. (a) is correct but (b) is wrong}\\
\text{4. Both (a) and (b) are wrong }
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