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ADDITIONAL FIBONACCI AND LUCAS FORMULAS

In Chapter 5, we found explicit formulas for both c08-math-001 and c08-math-002, namely, Binet's formulas. In this chapter we will derive additional explicit formulas for both [280].

8.1 NEW EXPLICIT FORMULAS

To begin with, we will conjecture an explicit formula for c08-math-003. To this end, recall that c08-math-004, so, as n gets larger and larger, c08-math-005; and hence c08-math-006. So we compute the value of c08-math-007 for the first ten values of n and then look for a pattern:

equation

The pattern might not be obvious; so we will go one step further. Add 1/2 to each, and see if a pattern emerges:

A pattern, surprisingly enough, does ...

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