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Yes, you can use your MacBook Pro on your power adapter while charging and after it has finished charging.

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This should answer most, if not all, of your battery questions:
Apple Notebook Battery FAQ by GGJstudios
The F.A.Q. includes the following topics:
  • BATTERY INFORMATION
  • BATTERY LIFE FROM A CHARGE
  • AC POWER
  • CALIBRATION
  • BATTERY LIFESPAN
  • CHECKING STATUS AND HEALTH
  • CHARGING
  • WHAT IS A CYCLE?
  • BATTERIES ARE NOT COVERED
  • BULGING OR SWELLING BATTERY

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To learn more about Mac OS X: Helpful Information for Any Mac User by GGJstudios
 
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