Can you tell me if my radius of convergences are correct?

myrautre

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Can you tell me if my radius of convergences are correct?

1. For the power série [imath]\sum_{k=1}^{\infty} \frac{k^2x^k}{k+1}[/imath] I found 1.

2. For the power série [imath]\sum_{k=0}^{\infty} k8^k x^{3k}[/imath] I found 1/2.

3. For the power série [imath]\sum_{k=0}^{\infty} 2^k x^{k^2}[/imath] I found 0 (I'm really not sure about this one).
 
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How did you get 0 for 3? E.g., would it converge for x = 1/2?
 
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