Series converges conditionally only if ratio test fails?

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It'd only just occurred to me that all conditionally convergent series must fail the ratio test - ie.

$$\sum^{\infty}_{n=0}a_n \,\,\,\text{conditionally converges}\implies{\lim_{n\rightarrow\infty}\left|\frac{a_{n+1}}{a_{n}}\right|=1}\lor{\lim_{n\rightarrow\infty}\left|\frac{a_{n+1}}{a_{n}}\right|\,\,\,\text{DNE}}$$

This surely must be a well-known consequence of the ratio test although I don't find it mentioned on Wikipedia/Wolfram. Is there a name for this result?

Or perhaps I've misinterpreted something incorrectly?