How do I calculate:

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- November 30th 2006, 11:10 AMa4sweDifference equation
How do I calculate:

- November 30th 2006, 11:34 AMtopsquark
- November 30th 2006, 11:41 AMa4swe
Yes, I would agree to that.

But what then? - November 30th 2006, 12:05 PMgalactus
You could start by building your iterations.

And so on and so on. - November 30th 2006, 12:15 PMa4swe
I want to have a formula for ANY n, that method won't help me.

I know there is one, and getting to that is my problem.

Is what I want it to be. - November 30th 2006, 03:07 PMtopsquark
(Hmmm...It seems I was off by a term in my earlier post. Galactus has it right.)

Have you tried an induction proof?

For n = 1:

Since this is good. (The formula also works for .)

So it works for some n. Let's see if it works for n + 1.

Now,

By hypothesis so

should be true.

On the LHS:

=

=

=

Similarly we may show that the RHS becomes

Which again gives:

So the two sides are equal.

So the theorem is true for n and n + 1 etc.

-Dan - December 1st 2006, 01:15 AMa4swe
Ahhh, yes!

Thank you tops.