Succesion $\displaystyle \{F_n\}\ n\geq0$ is defined $\displaystyle F_0=0, F_1=1, f_{n+2}=f_{n+1}+f_{n}$ (fibonacci). For each $\displaystyle n \epsilon $N (what's the command for natural numbers?)

Show for all $\displaystyle m\geq0:

\sum_{k=0}^{m}F_k^2 = F_m * F_{m+1}.$

This is what I have so far:

Induction plugging in 0 works.

$\displaystyle \sum_{k=0}^{m}F_k^2 + (m+1)^2 = F_m*F_{m+1} + (m+1)^2 = F_{m+1}*F_{m+2}$

$\displaystyle F_{m+1} * F_{m+2} = F_{m+1}*(F_{m+1} + F_m) = F_m*F_{m+1} + F_{m+1}*F_{m+1}$

As far as I got.