What is the radius of convergence of the power series ∑n=1&infty; (2n)!(n!)2 zn?

Find the radius of convergence of the series ∑n=1∞ (2n)!(n!)2 zn.

If f(x) is the sum of the power series 1 + 2x + 22x22! + 23x33! + ... on (-R, R), where R is the radius of convergence, what is the value of f(4)(0)?

Find the radius of convergence R of the power series ∑n=0∞ xn/(n+1).