I want to prove this :
But I've never approached a problem that required to mix functions and series. I guess I could use some notions on series convergence, but could anybody give me a head start or even just tips ? Thanks allis the domain of , and is the range of .
Let be some function, and let satisfy . Let a series be defined by :
Show that if this series converges towards a finite value, then it converges towards .
Note : you may use , with as an example.
This can be explained because then , yielding .