Kenneth Rosen Edition 7 Exercise 8.3 Question 7 (Page No. 535)

Question

Suppose that $f (n) = f (n/3) + 1$ when $n$ is a positive integer divisible by $3,$ and $f (1) = 1.$ Find

• A. $f (3)$
• B. $f (27)$
• C. $f (729)$

Answer 1

f(n)=f(n/3)+1                          f(1)=1

f(3)=f(3/3)+1 => f(1)+1 => 1+1=2

f(9)=f(3)+1 => 2+1=3

f(27)=f(9)+1 => 3+1=4

f(81)=f(27)+1=>5

f(243)=f(81)+1 => 6

f(729)=f(243)+1=>7