If you can show that it converges, then:
Take the limit of both sides of the recurrence.
Use the fact that
Solve for L.
I have this recurring function or whatever you call it:
Once increases, we have , inside of which there is another added and so forth (this clearly converges).
As the title says, I am looking forward to obtaining
P.S. I started from the greatest depth and noticed , however later on I am not able to control the expression...
P.P.S. Messing around I've got a good feeling that such infinite summations can be defined like that, no clue how to prove it though