10. (b) Give a closed form expression for can. (This should involve n, and should not explicitly involve any other element ak in the sequence.) (0) Describe this sequence using a recurrence relation. (This should describe how to obtain an from previous elements in the sequence.) . (Hunter, 3.2 #4) Consider the following recurrence relation: _ 0 if n = 0 0\"" 5an_1+1ifn21 Prove by induction that an : 57141 for all n 2 0. (Rosen, 5.2 #7) Which amounts of money can be formed using only twodollar-bills and vedollarbills? Prove your answer. Two strategies that may work include strong induction, or splitting into cases. . Let (in be the sequence dened by the following recurrence relation: 1 if n : 1 an : 7 if n : 2 Prove the following formula for on using strong induction. _ 3n + 5(1)\" L 2 . an . Let Q, (:2, 51:, y be complex numbers. Prove the following claim by strong induction: If (31:1: + 0211 if n : 1 on 2 C1332 + 02y2 if n = 2 (33 + y)an_1 xyan_2 if n 2 3 then an 2 can + 023;\" for all n 2 1. Use str0ng inductiori to prove the following formula for the Lucas numbers: 1+x/5n 1\\/5n Mr 2 H 2 )