An elementary question on radius of convergence.

Question

Is the radius of convergence of $\sum_{n=0}^{\infty} {z^{n^4}} $ = 1?

By definition it is the reciprocal of nth root of supremum of coeff of $z^n$, so should be 1 here. Am I correct?

I think, yes, you are correct. – Berci Apr 11 '13 at 10:16 — Berci, Apr 11 '13 at 10:16

score 2 · Accepted Answer · answered Apr 11 '13 at 10:18

2

Yes, $R^{-1}=\overline{\lim}_{n \to \infty} |a_n|^\frac{1}{n}=1 \implies R=1$

The sequence $\{|a_n|^\frac{1}{n} \}$ has infinitely many 1's and 0's. so its limit superior is 1

answered Apr 11 '13 at 10:18

user1337

1 Answers1