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#1 2007-11-24 07:18:49
- tony123
- Member
- Registered: 2007-08-03
- Posts: 229
F(1000)?
Let N = { 0, 1, 2, 3, ... } and suppose F: N --> Z+ is defined by: F(0) = 0 ; F(1) = 1 ;F(n) = 18F(n – 1) – 65F(n – 2), for all n = 2, 3, 4, ... What is F(1000)?
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#2 2007-11-24 07:40:54
- JaneFairfax
- Member
- Registered: 2007-02-23
- Posts: 6,868
Re: F(1000)?
First, you solve the characteristic equation.
The roots are 5 and 13. Hence
where A and B are constants. Substitute n = 0 and n = 1 to find A and B. You get A = −1⁄8, B = 1⁄8. ∴
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