- #1
huifei
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How to solve recurrence relation with one real root and two complex roots ?
The Example is ;
Solve the recurrence relation a n-1 + a n-3 = 0 where n ≥ 3 and a 1 = 1 a 2 = 1 a 3 = 2
a n = nth order
a n-1 = (n-1)th order.
a n-3 = (n-3)th order.
I've started the solving ;
a n = r^n
so
the equation will be ;
r^n - r^(n-1) - r^(n-3)
r^3 - r^2 - 1 = 0
I could'nt do anything after find the roots ?
What should i do ?
Thanks for helping.
The Example is ;
Solve the recurrence relation a n-1 + a n-3 = 0 where n ≥ 3 and a 1 = 1 a 2 = 1 a 3 = 2
a n = nth order
a n-1 = (n-1)th order.
a n-3 = (n-3)th order.
I've started the solving ;
a n = r^n
so
the equation will be ;
r^n - r^(n-1) - r^(n-3)
r^3 - r^2 - 1 = 0
I could'nt do anything after find the roots ?
What should i do ?
Thanks for helping.