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I have been meditating on this for a while, but can't seem to understand how this simplification came to be. Any help will be greatly appreciated.

So, here is what we start with:

##\mathop{\sum_{k=0}^m\sum_{l=0}^n}_{m{\geq}n} x(k,l)##

We also know that: l (lower case L) = n-m+k

and here is what my book ends with:

##\sum\limits_{k=m-n}^m x(k,n-m+k)##

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Here is my attempt, using the fact that l = n-m+k and substituting, I get:

##\mathop{\sum_{k=0}^m\sum_{n-m+k=0}^n}_{m{\geq}n} x(k,n-m+k)##

## = \mathop{\sum_{k=0}^m\sum_{k=m-n}^n}_{m{\geq}n} x(k,n-m+k)##

I then have no idea where to go from here : ( I tried substituting numbers for m and n and looked at what was happening, but that didn't help me much. Can someone please provide some insight please!!! I have been at this for a bit.

Thank you for reading.

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# Double sum of same variable simplification help

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