Discrete Math Problem Write out the values of F30 through F3

Discrete Math Problem

Write out the values of F3(0) through F3(8) for the following function. What does this function do? Can you express the value that it seems to be approaching?

Define F3(N)

   IF N=0

   RETURN 1

   ELSE RETURN SQRT(1 + F3(N-1))

Solution

Answer:

As said in the question if the value of N is 0, the function returns a value of 1. So we can derive the following values.

F3(0) = 1

F3(1) = SQRT(2) = 1.414

F3(2) = SQRT(1+SQRT(2)) = 1.553

F3(3) = SQRT(1+1.553) = 1.597

F3(4) = SQRT(1+1.597) = 1.611

F3(5) = SQRT(1+1.611) = 1.615

F3(6) = SQRT(1+1.615) = 1.618

F3(7) = SQRT(1+1.618) = 1.618

F3(8) = SQRT(1+1.618) = 1.618

The function is approaching the value of 1.618 as we move from F3(0) to F3(8).