Can the relationship between the series be proven using this information?

[ramsey2879]

Consider 3 series: A(0) = 0, A(1) = 4; A(n) = 6*A(n-1) - A(n-2) + 4; B(0)=1, B(1) = 3, B(n) = 6*B(n-1)-B(n-2) - 4; and C(0) = -1, C(1) = -11, C(n) = 6*C(n-1)- C(n-2) -4.

Is there a way to prove that the limit as n => infinity of A(n)/B(n) = -C(n)/A(n)?

Note that series C is actually series B run in reverse as C(0) = 6*B(0)-B(1) -4 and C(1) = 6*C(0) - B(0) - 4. Also, series A run in reverse is series A again as 0 = 6*0 -4 + 4 and 4 = 6*0 -0 + 4. That is ... -69, -11, -1, +1, +3 + 13 +71 ... is one series and ...28,4,0,0,4,28... is the corresponding series. Also, I have proven that C(n) = - B(n+1) + 2.

 

[berkeman]

Thread closed pending Moderation.

Please do not post schoolwork questions in the general technical math forums. Please do to now post solutions to schoolwork questions. Lordy.

 

[micromass]

Thread re-opened.

Ramsey2879: Please post such a questions in the homework forums next time. Even if it is not really homework, it is still in the style of a homework question so it belongs here.