AMC 12 2024b Problem 18

The Fibonacci numbers are defined by $F_1=1,$ $F_2=1,$ and $F_n=F_{n-1}+F_{n-2}$ for $n\geq 3.$ What is$$\dfrac{F_2}{F_1}+\dfrac{F_4}{F_2}+\dfrac{F_6}{F_3}+\cdots+\dfrac{F_{20}}{F_{10}}?$$ $\textbf{(A) }318 \textbf{(B) }319 \textbf{(C) }320 \textbf{(D) }321 \textbf{(E) }322$