Disproved: Crmarić and Kovač's 2025 theorem that every positive real number is the value of such a series for some $f(n)\to\infty$ is recorded on its claim page (Crmarić and Kovač, 2025). The site (page last edited 2025-09-28) labels the problem DISPROVED (LEAN) and credits them with the negative answer; the Lean proof behind the label is a public formalization of their argument linked from the claim page, not built or audited in this corpus. The variant with nondecreasing $f$, which the statement does not impose, remains open. The case $f(n)=n$ is answered yes: Kovač posted on the site's discussion thread (2026-07-12) that $\sum_n n!/(2n)!$ equals $\sum_n 1/(a_1\cdots a_n)$ with $a_k=4k-2$, a Cantor series with increasing integer terms, hence irrational. A manuscript of August 2026 extends the argument to $f(n)=an+b$ with $0\le b\le a$ and claims transcendence, hence irrationality, for every $a\ge1$ and $b\ge1-a$; it is a pending partial claim at Lambrinoudis 2026.