# Little problem

**Jorge Adriano
**
jadrian@mat.uc.pt

*Wed, 27 Mar 2002 16:29:59 +0000*

[moving to haskell-cafe]
>* Hello
*>* I have little problem. I want to solve this equation
*>*
*>* f(n-1) = f(n)+n
*>* f(6)=6
*
This is a simple recursive definition..
By the way, are you sure you didn't meant:
f(n-1)=f(n)+(n-1)
>* => f(2)=?
*
Not exactly sure what you're after here. You could simply do:
f(2)
=f(3)+3
=f(4)+4+3
=f(5)+5+4+3
=f(6)+6+5+4+3
=6+6+5+4+3
=24
anyway it's simple to see, or even prove by induction, that
f(n) = (\sum_{i=n+1}^{7} i) -1 = (n+8)(7-n)/2 - 1
If I'm rigth and you're formula is suposed to be
f(n-1) = f(n)+n
it is even easier.
J.A.