Question

Solve the following equation using generating function a_n − 5_an−1 + 6a_n−2 = 0, n ≥ 2 with boundary conditions a₀ = 1, a₁ = 1.

Answer 1

a_n - 5a_n-1 + 6a_n-2 = 0, n \(\geq\) 2

a₀ =a₁ = 1

∴ a₂ = 5a₁ - 6a₀ = 5 - 6 = -1

a₃ = 5a₂ - 6a₁ = -5 - 6 = -11

a₄ = 5a₃ - 6a₂ = -55 + 6 = -49

a₅ = 5a₄ - 6a₃ = -245 + 66 = -179

.

.