Fibonacci sequence empirical formula

[DavidGreen]

Homework Statement

Research the Fibonacci sequence and hence find the empirical or explicit formula for generating the nth term of the fibonacci sequence. Use this formula to show that it does indeed produce the Fibonacci numbers for n = 1 to 5. You may not use calculators, expansions of phiⁿ should be done by expanding and simplifying in surd form.

Homework Equations

Phiⁿ-(1- Phi)ⁿ / $\sqrt{}5$

Phi = 1+$\sqrt{}5$ / 2

The Attempt at a Solution

For N = 2
substitute A into B
Answers is wrong when expanded and simplified
Any help would be greatly appreciated
Cheers.

 

[Dick]

Homework Statement

Research the Fibonacci sequence and hence find the empirical or explicit formula for generating the nth term of the fibonacci sequence. Use this formula to show that it does indeed produce the Fibonacci numbers for n = 1 to 5. You may not use calculators, expansions of phiⁿ should be done by expanding and simplifying in surd form.

Homework Equations

Phiⁿ-(1- Phi)ⁿ / $\sqrt{}5$

Phi = 1+$\sqrt{}5$ / 2

The Attempt at a Solution

For N = 2
substitute A into B
Answers is wrong when expanded and simplified
Any help would be greatly appreciated
Cheers.

It should work fine. You'll have to explain what's going wrong.