Solve these recurrence relations together with the initial conditions given. (a)an =an−2 forn≥2,a0 =5,a1 =−1.
(b)an+2 =−4an+1+5an,forn≥0,a0 =2,a1 =8.
Find the solution to an = 2an−1 + an−2 − 2an−3 for n = 3,4,5,…, with a0 = 3, a1 =6,anda2 =0.
Solve the recurrence relation an = 6an−1 − 12an−2 + 8an−3 with a0 = −5, a1 = 4, and a2 = 88.
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Consider the nonhomogeneous recurrence relation an = 2an−1 + 2n. (a) Show that an = n2n is a solution of this recurrence relation. (b) Find all solutions of this recurrence relation.
(c) Find the solution with a0 = 2.
1/2 CSI2101/UOttawa/MdH/W22
What is the general form of the particular solution guaranteed to exist by The- orem 6 of the linear nonhomogeneous recurrence relation an = 6an−1 − 12aa−2 + 8an−3 + F (n) if
(a) F(n) = 3? (b) F(n) = n2? (c) F(n) = 2n? (d) F(n) = n22n?
2/2 CSI2101/UOttawa/MdH/W22
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