Consider the "Retirement Series", so named because the coefficients of its recurrence correspond to the "standard" retirement age of 65: R(0) = 0, R(1) = 1, R(n) = 6R(n-1)-5R(n-2) for n > 1 [a] Explain why the recurrence is considered to be "linear homogeneous". [b] State the characteristic equation of the recurrence [c] Using the methods of our course, derive a closed-form formula for R(n). [d] For the case n = 2, test your formula for R(n) against the original recurrence.