is there a way of turning recursive equations of the form where into an explicit form with variables a, b and c?

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- May 27th 2009, 04:38 PMRubberduckzillarecursive to explicit equations
is there a way of turning recursive equations of the form where into an explicit form with variables a, b and c?

- May 27th 2009, 07:36 PMputnam120
, easy induction proof.

- May 27th 2009, 09:17 PMSoroban
Hello, Rubberduckzilla!

I know one way . . . it's rather long . . .

Quote:

Is there a way of turning recursive equations of the form .

where into an explicit form with variables ?

Subtract

. . and we have: .

Let: .

Divide by

. . which factors: .

. . and has roots: .

Hence, the function contains: .

The function is of the form: .

We determine and by using the first two terms of the sequence.

Subtract

. .

Substitute into

Therefore: .