The second Fibonacci number is 1, so it's reciprocal should be 1, right? Why is it that I get $-1$ when I plug in $2$ for n in the reciprocal of Binet's equation
$$\frac{1}{F_n}=\frac{\sqrt{5}}{\varphi^{-n}-(-\varphi)^n}$$
I think I may have messed up on the algebra when reducing but can't find any error. Please help!