- #1
dodo
- 697
- 2
How would you go on proving the following conjecture?
Given
Given
[tex]
S_0 = 0, \quad S_1 = 1, \quad S_n = a S_{n-1} + b S_{n-2}
[/tex]
Prove thatS_0 = 0, \quad S_1 = 1, \quad S_n = a S_{n-1} + b S_{n-2}
[/tex]
[tex]
{ S_n }^2 - S_{n-1} S_{n+1} = (-b)^{n-1} \quad (n = 1, 2, 3, ...)
[/tex]
{ S_n }^2 - S_{n-1} S_{n+1} = (-b)^{n-1} \quad (n = 1, 2, 3, ...)
[/tex]