- #1
Nono713
Gold Member
MHB
- 618
- 4
Just an easy one to start off with, find a non-recursive formula for the $n$th term of the following linear homogeneous recurrence:
$$a_0 = 2, ~ ~ a_1 = -2, ~ ~ a_n = -2 a_{n - 1} + 2 a_{n - 2} ~ ~ \text{for} ~ n \geq 2$$
$$a_0 = 2, ~ ~ a_1 = -2, ~ ~ a_n = -2 a_{n - 1} + 2 a_{n - 2} ~ ~ \text{for} ~ n \geq 2$$
Hint:
You can use generating functions to solve this problem.