2 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 $n\geq 4$.