calculus limits

Question

you're given a hundred dollars at the beginning of day 1 at the end of the day you have to give back half of your holdings for each day there after you are given another $100 and at the end of each day you have to give back half of your holdings. what is the limit of your holdings at the end of each day as time goes on indefinitely?  I understand a little how I should set this up, but I'm confused. Would indefinitely represent infinity? I need help on this. I got the answer, but I don't know how to create the formula.

Answer 1

As I read the conditions (and I may be in error), the series is not convergent, it does not have a limit. Note:

 

Start of day            End of Day

100                        50

150                        75

175                        87.50

187.50                   93.75