Simplifying Linear Second Order Recurrence sequences...
Posted on 2011-03-13
I'm not sure how to write the correct subscript notation for this expression, but I've got a sequence
Un = (some expression)
and need to prove an identity, where the LHS has Un+1 Un-1 - (Un)^2
(where n, n+1 and n-1 are all subscripts of U)
By multiplying out the expression substituting in n, n-1 and n+1 I have been able to cancel out a number of terms, but have some left that I can't simplify.
In the expression below there are no subscripts, everything is superscript:
9^(n-1).(-2)^(n+1) + (-2)^(n-1).9^(n+1) - 2(9^n (-2)^n)
is it possible to simplify this any further?