C.1. The function F:Z+Z+is defined recursively as follows: F(1)=1,F(2)=2, and F(n)=F(2n)+F(2n)1 for n3. (i) Calculate the value of F(9). (ii) Use strong induction to prove that F(n)n for every positive integer n. (Suggestion: Recall the inequalities for floor and ceiling functions in Table 1 in Section 2.3.).

1. C.1. The function F:Z+Z+is defined recursively as follows: F(1)=1,F(2)=2, and F(n)=F(2n)+F(2n)1
for n3. (i) Calculate the value of F(9). (ii) Use strong induction to prove that F(n)n for every positive
integer n. (Suggestion: Recall the inequalities for floor and ceiling functions in Table 1 in Section
2.3.)