F(n)=(-1)n2n

Solution for F(n)=(-1)n2n equation:

(F)=(-1)F2F

We move all terms to the left:

(F)-((-1)F2F)=0


We calculate terms in parentheses: -((-1)F2F), so:

(-1)F2F

We multiply parentheses

-1F^2

Back to the equation:

-(-1F^2)


We get rid of parentheses

1F^2+F=0

We add all the numbers together, and all the variables

F^2+F=0

a = 1; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·1·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*1}=\frac{-2}{2}
=-1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*1}=\frac{0}{2}
=0
$