Engineering Optimization: Theory and Practice, Fourth Edition

5.8 Golden Section Method 269

Figure 5.10 (continued)

This result can be generalized to obtain

Lk= iml

N →∞

(

FN− 1

FN

)k− 1

L 0 (5.19)

Using the relation

FN=FN− 1 +FN− 2 (5.20)

we obtain, after dividing both sides byFN− 1 ,

FN

FN− 1

= 1 +

FN− 2

FN− 1

(5.21)

By defining a ratioγas

γ= lim

N →∞

FN

FN− 1

(5.22)