[SLUG] project

[Gavin Baker]

On 9 Jun 2006, at 10:17, Stephen O'Neill wrote:

> Bob Garrood wrote:
>> # A is for amount borrowed, n for number of years and i the annual  
>> interest rate.
>> m=n*12
>> r=(1+i/1200)
>> p=A*r^(m-1)*(r-1)/(r^m-1)
>> {print p}
>
> The thing that I didn't know how to express here was Pn without a  
> recursive loop for the sum - which seems to be what your formula  
> solves.

I guess you have these, but I will throw em in anyway


Arithmetic sequence

   x(1) = a,  x(n+1) = x(n)+d   (for n=1,2,3,...)

has closed form

   x(n) = a + (n-1)d   (n=1,2,3,...)


Geometric sequence

   x(1) = a, x(n+1) = rx(n)  (n=1,2,3,...)

has closed form

   x(n) = ar^(n-1)  (n=1,2,3,...)


Linear sequence

   x(0) = a, x(n+1) = rx(n) + d  (n=0,1,2,...)

has closed form

   x(n) = (a + d/(r-1))r^n - d/(r-1)  (n=0,1,2,...)


Exponential model

   P(n+1) = (1+r)P(n)  (n=0,1,2,...)

has closed form

   P(n) = (1+r)^nP(0)  (n=0,1,2,...)


There are simple ways to derive all these, and all linear recursion  
sequences have a closed form. Google or wikipedia for Binet's formula  
for the most famous...

> Oh, and MathML in HTML anybody?

I didn't have much fun with MathML, even with apps I have that can  
export it (mathematica/maple)

LaTeX chunks as images looks nicer and work everywhere.

If you wanna show off, you could even use aamath to set the title  
attribute of the images!


Gav