Talk:Radius of Convergence from Limit of Sequence/Real Case

$1/R = 0$
The condition $1/R = 0$ as stated in the Theorem is, of course, gibberish mathematically. (It seems odd that there is a comment at the bottom saying that the alternative definition of R would be "less convenient".) However, I assume that this was copied from the original source. Are we therefore required to keep it as is? KarlFrei (talk) 09:55, 14 November 2018 (EST)
 * Page 144 of Binmore (cited on this page) gives it like this, but qualifies with "appropriate conventions must be adopted if the right hand side of the formula happens to be $0$ or $+\infty$. I think it is easily rectified by just writing $\displaystyle \lim_{n \mathop \to \infty} \size {\frac {a_{n + 1} } {a_n} } = 0$ without the $\dfrac 1 R$ as in the Cauchy-Hadamard Theorem, and writing some justification in the body of the proof. Caliburn (talk) 11:42, 14 November 2018 (EST)