 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2018/discrete-mathematics-continuous-mathematics-and-probability/7/c/iii/solution

(r - 2)^{2}

, so its repeated-root solutions are

(A + B n) 2^{n}

. A constant particular solution is one. Thus

u_{n} = 1 + (A + B n) 2^{n}

A = - 1

and

B = 1

, hence

u_{n} = 1 + (n - 1) 2^{n} .

The factor

n

is required by the repeated root of a polynomial; omitting it would lose one independent solution.

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