Re: FACTORIALS BY Algorithm -please comment

In article <1150492189.066413.45760@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"abose" <hirak99@xxxxxxxxx> wrote:

Let P(x) be a polynomial of degree n. Let the coefficient of x^n be a.
Then notice that P(x+1)-P(x) is a polynomial of degree n-1, and the
coefficient of x^(n-1) is n*a.

Using the above fact and induction, you can see that you will end up
with Factorial(m) when you start with P(x)=x^m (or for that matter, any
monic polynomial of degree m) at the second row, and repeatatively
replace P(x) by P(x+1)-P(x).


dave wrote:
using excell
I created a matrix

Row1 : 1 2 3 4 5 ....
Row2: A1^2 B1^2 C1^2....
Row3: (B2-A2) (C2-B2)...
Row4: Factorial !!!!

I find that for any power the above method will "converge" to the factorial
of "n" in n+2 rows where n=the power. What is the method I stumbled on
called?

"Finite Differences"

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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    ... Let the coefficient of x^n be a. ... Then notice that P-Pis a polynomial of degree n-1, ... dave wrote: ... Row4: Factorial!!!! ...
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