The Fibonacci numbers are defined by $F_1=1,F_2=1$, and $F_n=F_{n-1}+F_{n-2}$ for $n\ge 3$. The Lucas numbers are defined by $L_n=F_{n-1}+F_{n+1}$ for $n\ge 1$. What is

$\frac{F_{10}}{F_5}+\frac{F_{12}}{F_6}+\frac{F_{14}}{F_7}+\dots +\frac{F_{30}}{F_{15}}$?