On 2/5/2013 11:05 AM, Jim Thompson wrote:
It's been too long ago, I can't remember how to reduce difference
equations.

Suppose I have...

f(N+1) = 0.97*f(N)

Now I know, off the seat of my pants (I think :-), that...

f(N) = Const*(0.97^N)

But I can't remember how to rigorously get to that conclusion.

...Jim Thompson


You've received good answers so far, but another way to do it is through
generating functions. The differential equation for the "exponential
generating function" of this recurrence can be written by inspection;
it's y' = 0.97*y.

Assuming F(0) = 1, the solution to this differential equation is y =
e^(0.97*x). The solution to your recurrence is then the coefficient of
x^k/k! in the Taylor series expansion of e^(0.97*x), or 0.97^k.