- #1
roam
- 1,271
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Homework Statement
http://img10.imageshack.us/img10/8418/56729818.gif
The Attempt at a Solution
Firstly do I need to use the "simple induction" or "complete induction"?
I will try the simple induction.
Base Case: [tex]P(1) = f_1 f_0 - f_{1}^2 = (-1)^1[/tex]
We don't know what the value of [tex]f_0[/tex] is, but if [tex]f_0 = 0[/tex] we get [tex]1 .0 - 1=-1[/tex]. Therefore P(1) is true.
Inductive Step: Suppose P(k) is true, where [tex]k \in N[/tex]. Now I'm stuck & don't know how to deduce that P(k+1) is true.
i.e. show that [tex]P(k+1) = f_{k+1}.f_k - f^2_{k+1}=(-1)^{k+1}[/tex] is true.
any help or clues here is very appreciated
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