- #1
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Homework Statement
sketch on the complex plane the region where the following two power series both converge
1) sigma from n=0 to infinity [(z-1)^n]/[n^2]
2) sigma from n=0 to infinity [((n!)^2)((z+4i)^n)]/[2n]!
The Attempt at a Solution
R=lim as n tends to infinity |(a(subscript n))/(a(subscript n+1))|
1) R=lim n tends to infinity [(z-1)^n][[n+1]^2]/[n^2][[z-1]^(n+1)]
=((n+1)^2)/(n^2)(z-1)
2) R=lim as n tends to infinity [((n!)^2)((z+4i)^n)/(2n)!][(2(n+1))!/(((n+1)!)^2)((z+4i)^(n+1))
I don't know how to proceed from here and I think I may have made a mistake somewhere