Prove that for all positive integers. I assume the solution involves induction, but I'm having trouble with this... Any pointers would be greatly appreciated. Thanks
Follow Math Help Forum on Facebook and Google+
Originally Posted by VinceW Prove that for all positive integers. I assume the solution involves induction, but I'm having trouble with this... Any pointers would be greatly appreciated. Thanks Yes, this involves induction. For n = 1, we have "2 = 1 + 1". For n >= 1, let's identify what we are trying to prove... i.e. Now use the definition of the Fibonacci sequence, and see what comes up (should/might involve some distribution)...
Originally Posted by VinceW Prove that for all positive integers. I assume the solution involves induction, but I'm having trouble with this... Any pointers would be greatly appreciated. Thanks I suppose induction can be used here, but if you know the relation , then the solution is straighforward, though you need to play algebraically quite a while with the resulting expressions. Tonio
Proof, without induction (?) Define so (by induction) General case Proof we have the matrix identity so by multiplication of the matrices take so