Fibonacci using proof by induction: $\sum_{i=1}^{n-2}F_i=F_n-2$ everyone.
I have been assigned an induction problem which requires me to use induction with the Fibonacci sequence. The summation states:

$$\sum_{i=1}^{n-2}F_i=F_n-2\;,$$ with $F_0=F_1=1$.

I have tried going through the second one to see if it was right, but I came with a weird thing. $F_2$ should be $2$, but according to this statement, it equals zero.
What am I doing wrong? It got my attention.
Thank you for your time.

The sum of $F_i$ where $i$ is greater than equal to $1$ and less than or equal to $2-2=0$ is $0$--the so-called empty sum--which also happens to be $2$ less than $F_2=2,$ so it holds in the $n=2$ case. It does not hold for the $n=0,1$ cases, by the way. The lowest case for which it can be said to hold is $n=2$.
