Kenneth Rosen Edition 7 Exercise 8.3 Question 9 (Page No. 535)

Question

Suppose that $f (n) = f (n/5) + 3n^{2}$ when $n$ is a positive integer divisible by $5, \:\text{and}\: f (1) = 4.$ Find

• A. $f (5)$
• B. $f (125)$
• C. $f (3125)$

Answer 1

f(5):

$f(5) = f(5/5) + 3(5)^{2}$

=$ f(1) + 3(25)$ 

= $4 + 75$

= $79$

 

f(125):

$f(25) = f(25/5) + 3(25)^{2}$

= $f(5) + 3(625)$ 

  = $79 + 1875$ 

= $1954$

$f(125) = f(125/5) + 3(125)^{2}$

= $f(25) + 3(15625) $

= $1954 + 46875$

= $48829$

 

f(3125):

$f(625) = f(625/5) + 3(625)^{2}$

= $f(125) + 3(390625)$

= $48829 + 1171875 $

= $1220704$ 

$f(3125) = f(3125/5) + 3(3125)^{2}$ 

=$ f(625) + 3(9765625) $

= $1220704 + 29296875$

= $30517579$