4 problems

Sun's ratio monotonicity conjecture. The sequence $\{S_{n+1}/S_n\}_{n\geq 3}$ is strictly increasing to the limit $9$, and the sequence…

Ratio log-concavity conjecture. The sequence $\{r_n\}_{n\geq 4}$ is log-concave, equivalently, $R_n$ is ratio log-concave for $n\geq 4$.

Strong ratio monotonicity conjecture. The sequence

Infinite strict ratio-monotonicity conjecture. The Boros-Moll sequence $\{d_i(m)\}_{0\leq i\leq m}$ is $\infty$-strictly-ratio-monotone.