2:05 AM
But the question is vague and nonprecise
It looks like one I'd delete

Well, it should be closed then. If there is an answer, there is no way to get rid of the question besides closing it.

5 hours later…
7:03 AM
[ SmokeDetector ] Few unique characters in answer: Define function J by kristin on math.stackexchange.com

2 hours later…
9:21 AM
I dodn't notice the answer there. Actually it is a duplicate; I flagged it and it hasn't see light for past one week.
2

So I've been thinking through some test cases. If $a_n = n$ then $\sum_n \frac{a_{n+1} - a_n}{a_n}$ is the harmonic series which diverges. And if $a_n = \sum_{k=1}^n 1/k$ then $\sum_n \frac{a_{n+1} - a_n}{a_n}$ diverges like $\sum_n 1/(n \log n)$. So that got me thinking, if $a_n$ is a strictly i...

...and many more (I had quoted 4 of them above; unable to decide which all to be flagged)
Looks like this duplicate I quoted was asked 20mins after Maryann's question, and better received than her's!