9. Suppose that {an} satisfies the linear nonhomogeneous recurrence relation
an = c1an−1 + c2an−2 + · · · + ckan−k + f(n)
where c1, c2, . . . , ck are real numbers, and f(n) = (btn
t + bt−1n
t−1 + · · · + b1n + b0)s
n
,
where b0, b1, . . . , bt and s are real numbers.
Case (i): When s is not a root of the characteristic equation of the associated linear
homogeneous recurrence relation, there is a particular solution of the form (ptn
t +
pt−1n
t−1 + · · · + p1n + p0)s
n
.
Case (ii): When s is a root of the characteristic equation of the associated linear
homogeneous recurrence relation with multiplcity m, there is a particular solution of
the form n
m(ptn
t + pt−1n
t−1 + · · · + p1n + p0)s
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