- #1

- 7

- 0

## 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?

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

- Thread starter StellaLuna
- Start date

- #1

- 7

- 0

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?

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

- #2

- 10

- 0

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.

- 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