On monotonicity of some combinatorial sequences

Qing-Hu Hou, Zhi-Wei Sun, Haomin Wen

We confirm Sun's conjecture that $(\root{n+1}\of{F_{n+1}}/\root{n}\of{F_n})_{n\ge 4}$ is strictly decreasing to the limit 1, where $(F_n{)}_{n\ge 0}$ is the Fibonacci sequence. We als…