@Kitonum That is some nice disassembly of the function in Addition 2.
In Addition 1 I found using the inert form Sum and then setting u=v gives the correct evaluation of the limit.
I was originally trying to convert that expression automaticially to the sum for an abrtitary m. An example of something similar is which assuming n>m can be represented as but outside of actual numbers I can't get Maple to factor to that. That then evaluates to .
These functions are rather elementry and I am surprised Maple doesn't seem handle this.
In the original document I attached, I notice something odd with
The second sum is from 0 to infinity. How could that be?
Edit:- How do you do those nice grey sections where you display your code?