Solve first order difference equation

[toofle]

Homework Statement

Solve the first order difference equation.

Homework Equations

x[n] - x[n-1] = n(n+1)/2
x[1] = 1

The Attempt at a Solution

Homogenous solution:
Characteristic equation:
r - 1 = 0 <=> r = 1
=> yhn = C * 1^n = C

Particular solution:
ypn = ?
I'm supposed to do some intelligent guess here. n(n+1)/2 is a polynomial of degree 2 and doesn't exist in yhn so i should be something like An(n+1) or An^2+Bn but Ican't get anything to work.

 

[Dick]

I would guess a polynomial of order 1 degree higher than n(n+1)/2. Say An^3+Bn^2+Cn.