### Comment:
https://www.wolframalpha.com/input/?i=sum+2%5E-j,+j%3D1+to+10000

### REPLY:
It only actually equals 1 if n is infinity. If n is anything less than infinity then it is an approximation.  
  
 So for a real world application like this, n obviously isn’t infinity so if he loses 12% every day then his account will never actually equal zero (even though 1/100000th of a cent is essentially zero).

### END.