Error propagation in a Fibonacci calculation

You compute Fibonacci numbers $F_0,\dots,F_{99}$ correctly but record $F_{100}$ as $G_{100}=F_{100}+1$. You then keep applying the recurrence to your recorded values to obtain $G_{101},\dots,G_{110}$. What is $G_{110}-F_{110}$?

89. The error $e_n=G_n-F_n$ obeys the same recurrence, with $e_{99}=0$ and $e_{100}=1$. So $e_n=F_{n-99}$, and $e_{110}=F_{11}=89$.