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**tokio** Sorry for all of these induction promblems, i have a couple of more questions, and as an respected remember recommended, i will attempt these promblems.

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Define the sequence F as follows:

$\displaystyle F_1=1, F_2=1, F_n=F_n-1 + F_(n-2) n >= 3 $

Prove that

$\displaystyle F_1^2+F_2^2+... F_n^2 = F_nF_(n+1) whenever n is a positive integer.$

Here is what i did

1. P(n): $\displaystyle F_1^2+F_2^2+... F_n^2 = F_nF_(n+1)$

2. P(3) $\displaystyle F_3^2 = F_3F_3+1 $ Im confused on this step, i got $\displaystyle F_9 = F_3F_4 $

3. Assume: P(n): $\displaystyle F_1^2+F_2^2+... F_n^2 = F_nF_(n+1)$

4. Prove P(n+1)

$\displaystyle F_n+F_n+1+F_(n+1)^2 = F_n+1F_n+2$ // replaces right hand side of the original equation up to teh summation of the left hand side

$\displaystyle f_n+1[F_n+F_n+1+F_n+1 = F_n+1F_n+2 $ // Factored out $\displaystyle F_n+1$. Im stucked, i need pointers on step 2 and 4, thanks.