Changing the order of triple summation

[hjcho]

Homework Statement

I want to change the order of triple summation. it follows:
$$\sum^N_{k=0} f(k) \sum^k_{n=0}\sum^{N-k}_{m=0} g(k,n)h(k,m)A(n+m)$$

=>
I need to set the variable x(=n+m) go from 0 to N firstly, and then further go on...
$$\sum^N_{x=0} A(x) \cdots \cdots$$

But, I don't know how... please answer this question.
Thank you very much

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

welcome to pf!

hi hjcho! welcome to pf!

$$\sum^N_{k=0} f(k) \sum^k_{n=0}\sum^{N-k}_{m=0} g(k,n)h(k,m)A(n+m)$$

let's write it in ordinary english …

k can be anything (up to N), but n must be less than k, and m+k can be anything (up to N)

ok, so how would we write it if we started with m? ​

(hmm … are you sure that last N, above the ∑, shouldn't be an n ? )