Question of the Complex Analysis

$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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