If you can show that it converges, then:
Take the limit of both sides of the recurrence.
Use the fact that
to get
Solve for L.
Hello.
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
If
then taking limits in both menbers,
and necessarily the limit is the positive solution.
Fernando Revilla
Edited: Sorry, I didnīt see snowtea's post.
It is esay to prove that is increasing. To prove that is bounded we can use
where is the positive root of and the negative one.
Fernando Revilla