- #1
perplexabot
Gold Member
- 329
- 5
Hello all,
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)##
-----------------------------------------------------------------------------------
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.
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)##
-----------------------------------------------------------------------------------
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.