2.84 You were introduced to Egyptian fraction expressions in subsection 2.8.2. If q is a rational number strictly between 0 and 1, then an Engel expansion for q is an Egyptian fraction expression of the form 1 9= + 1 + 02 + a02...ak a1 1 + + + where the a; are natural numbers and aj s a2 <...ak. for example explain why the assumption that tells us aj> 2, that is, aj #1. (b) Find an Engel expansion for 17/20. (c) Devise a greedy algorithm that will produce the Engel expansion for any rational number between 0 and 1. (d) Prove that every rational number between 0 and 1 has a finite Engel expansion. That is, prove that the method you just devised in part (c) actually works. This might be harder than proving that Fibonacci's greedy algorithm works. (e) We know that Egyptian fraction decompositions are not unique. Are the more specialized Engel expansions unique? 2.84 You were introduced to Egyptian fraction expressions in subsection 2.8.2. If q is a rational number strictly between 0 and 1, then an Engel expansion for q is an Egyptian fraction expression of the form 1 9= + 1 + 02 + a02...ak a1 1 + + + where the a; are natural numbers and aj s a2 <...ak. for example explain why the assumption that tells us aj> 2, that is, aj #1. (b) Find an Engel expansion for 17/20. (c) Devise a greedy algorithm that will produce the Engel expansion for any rational number between 0 and 1. (d) Prove that every rational number between 0 and 1 has a finite Engel expansion. That is, prove that the method you just devised in part (c) actually works. This might be harder than proving that Fibonacci's greedy algorithm works. (e) We know that Egyptian fraction decompositions are not unique. Are the more specialized Engel expansions unique