Question

Find the radius of convergence of the power series P 8

n=1

(z−i)ⁿ/
n²


thanks my answer I will return​

Answer 1

) Let un=z3n2n so

|un+1un|=2n|z|32n+2→|z|3<1⟺|z|<1

so

R=1

(ii) Let vn=(2n+i)(z−i)n so

|vn+1vn|=|(z−i)(2n+1+i)2n+i|→2|z−i|<1⟺z∈D(i,12)

so

R=12

(iii) Let wn=zn! so

|wn+1wn|→ℓ=0⟺|z|<1

so

R=1

Answer 2

Explanation:

Dinesh bro

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