Fibonacci Numbers

  • Thread starter StellaLuna
  • Start date
  • #1

Main Question or Discussion Point

Could anyone help me with the following proof?

F^2_n + F^2_(n+1) = F_(2n+1) for ngreater than or equal to 1?
 

Answers and Replies

  • #2
10
0
I think a good technique would be to use induction (I don't know if it actually works, I haven't done the proof).

You first consider a base case, in this case it would be n = 1. Check to see that for this the formula works.

Then comes the inductive step. Assume that this formula works for n =k, and then prove that it works for n = k+1.

Then you're done. The reason this proof works is that truth for n=1 implies truth for n=2, and then n=3, and so on infinitely, so the formula would work for all n.
 

Related Threads on Fibonacci Numbers

Replies
15
Views
2K
Replies
0
Views
2K
Replies
2
Views
2K
  • Last Post
Replies
1
Views
7K
  • Last Post
Replies
2
Views
258
  • Last Post
Replies
1
Views
2K
Top