Hi, I am trying to solve the following limit:

where

with provided initial conditions. I have solved the recurrence relationship, and the specific solution does contain two terms:

I've tried a few tricks to simplify the log expression, including:

and was able to modify this expression to bound the limit, but haven't been able to obtain the limit itself.

I have also tried to compute the limit directly on the recurrence relationship (rather than solving it first) but ran into similar problems with log(A+B) terms. Any suggestions on how to proceed?