I'm really shaky with radius of convergence and limits when complex numbers are thrown into the mix, so I would be really grateful if someone could check I've answered these questions correctly! (I can't find any examples online that are quite as complicated)
1. Find the limit of (2n*e(( ln(n^2) + i*pi*n )/(( 16(n^2) + 5i ))^0.5))/((4n2 + 3in)(1/2)) [From n=1 to infinity]
2. Compute the radius of convergence of the power series: (sum from n=1 to infinity) of anzn, where an = (2n + 1)!(n + 2i)n/(3n)!
My answers: 1. The limit does not exist. 2. R=27/4
Help would be veeeery much appreciated!