Here is a way:
With[{m = 16}, vls = Solve[Flatten@Table[{ f[x] + g[4 - x] == 4, g[4] == 8, g[x] - f[x - 8] == 8, g[4 + x] == g[4 - x]}, {x, -2 m, 2 m}]]; Sum[f[2 k], {k, m}] /. vls[[1]]]
Thank you! What is the meaning and function of this code?
Flatten@Table[{f[x] + g[4 - x] == 4, g[4] == 8, g[x] - f[x - 8] == 8, g[4 + x] == g[4 - x]}, {x, -32, 32}]
If you're going to post the same question as you did on another forum, you really need to provide a link to that question as you can be wasting the time of folks trying to help you that don't know there might be informative comments or even answers.
https://mathematica.stackexchange.com/questions/302375/how-to-find-the-cumulative-value-through-the-abstract-function-analytic-expressi
