SEAMO 2026 Paper D SET 2 – Self-practice Question 21

Given $Q_{n+1}=\frac1{1+1/Q_n}$ for $n=1,2,3,4,\ldots,2017,2018$ and $Q_1=1$, evaluate $Q_1Q_2+Q_2Q_3+Q_3Q_4+\cdots+Q_{2017}Q_{2018}$.