Consider the sequence {an}n≥1 defined as follows: a_1 \equal{} 1, a_{2k} \equal{} 1 \plus{} a_k and a_{2k \plus{} 1} \equal{} \frac {1}{a_{2k}} for every k≥1. Prove that every positive rational number appears on the sequence {an} exactly once. searchinductionalgorithmcontinued fractionnumber theoryEuclidean algorithmalgebra proposed