How does $-(-1)^n$ become $(-1)^{n+1}$ I am currently studying how to prove the Fibonacci Identity by Simple Induction, shown here, however I do not understand how $-(-1)^n$ becomes $(-1)^{n+1}$.  Can anybody explain to me the logic behind this?

The powers of $-1$ are $$-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, \ldots$$ If $n$ is odd, then $(-1)^n = -1$, but if $n$ is even then $(-1)^n = 1$. So if you multiply $(-1)^n$ once by $-1$, it is the same as incrementing $n$. (Technically you can also decrement, but you can't generalize that to other negative numbers).
