Talk:Sum of nth Fibonacci Number over nth Power of 2/Proof 4

Error in showing $S$ is absolutely convergent

There is a minor error in showing that $S$ is absolutely convergent. Although the limit of the ratios in the ratio test is less than 1, it is not because $F_n + F_n > F_{n-1} + F_n$. One can have sequences $b_n > a_n$ such that $\lim_{n\to\infty} \frac{a_n}{b_n} = 1$. The easiest fix is to note that $\lim_{n\to\infty} \frac{F_{n+1}}{2F_{n}} = \frac{\phi}{2} < 1$ where $\phi$ is the golden ratio. --Inf-dim (talk) 02:11, 30 December 2023 (UTC)