Question 2
Two operations $L$ and $R$ are defined as follows on rational numbers $p/q$, where $p$ and $q$ are positive integers:
$$L\left(\frac pq\right)=\frac p{p+q},\qquad R\left(\frac pq\right)=\frac{p+q}q.$$
Start from 1 and apply the operations $R,L,R,L,R,L,R,L,R,L$ successively. When the result is written as a fraction in simplest form, what is the sum of its numerator and denominator?
$$L\left(\frac pq\right)=\frac p{p+q},\qquad R\left(\frac pq\right)=\frac{p+q}q.$$
Start from 1 and apply the operations $R,L,R,L,R,L,R,L,R,L$ successively. When the result is written as a fraction in simplest form, what is the sum of its numerator and denominator?