For the recurrence an=an−1+an−2+⋯+a0a_n = a_{n-1} + a_{n-2} + \dots + a_0an=an−1+an−2+⋯+a0, what is the characteristic equation?
rn−rn−1−⋯−1=0r^n - r^{n-1} - \dots - 1 = 0rn−rn−1−⋯−1=0
r2−2r+1=0r^2 - 2r + 1 = 0r2−2r+1=0
r2−r−1=0r^2 - r - 1 = 0r2−r−1=0
rk−rk−1−rk−2−⋯−1=0r^k - r^{k-1} - r^{k-2} - \dots - 1 = 0rk−rk−1−rk−2−⋯−1=0