This problem is in the context of discrete systems and signals.

My goal is to find an equation for y(n) without the summation.

\(y(n)=\sum_k k(n-k)u(k-4)u(k+2-n)\)

where \(u(k)\) is the unit step function, k is from -inf to inf, and n=0,1,2,3...

So I need to eliminate the unit step functions from the equation by changing the limits of summation:

if \(k-4\geq 0\) then \(u(k-4)=1\). And so it's eliminated from my summation above.
if \(k+2-n\geq 0\) then \(u(k+2-n)=1\). And it's also eliminated.

So my limits of summation are \(k\geq 4\) and \(k\geq n-2\). But the limits don't define a finite range! Can anyone help?

 

You don't say whether the summation over k is over a finite or infinite range nor what the domain of n is. If it is infinite, the series clearly diverges -- you can ignore the step functions for large enough k and you're then summing terms of the form nk - k^2.

If you remember the step function isn't unity until the argument is >= 0, then you can see the only relevant terms will be whichever of k >= 4 or k >= n+2 is larger; the smaller terms will be zero because the step function is "switched off". Then you should be able to write down closed form expressions because nƩk and Ʃk^2 are easy to find in a handbook.

BTW, it's k >= n - 2.